mm-659 === Subject: find number of homomorphism f such that f : Q(sqrt(-2)) -> Q(i , sqrt(2)) it's easy?? but i can't~ let me advice, please thank you. sir~ === Subject: Re: @.@ um...difficult~ > find number of homomorphism f such that > f : Q(sqrt(-2)) -> Q(i , sqrt(2)) > ---------------------------------- > um....... > it's easy?? Yes: f(a + b.sqrt(-2)) = a + b.i.sqrt(2). Jose Carlos Santos === Subject: Re: derivative of a function > I see technologically illiterate people using `magic' every day -- they > just consider the items to be ``black boxes'' and proceed with their jobs, > lives, and interests. I find it amusing to watch high energy physicists > treating computer systems thus. In most ways, these scientists are very > literate; but computers and their systems are not always something that > they feel a need to learn how they function -- only how to use them to > do the functions they want done. >How do you feel about licensing requirements for automated computation >systems? Should Assembly be part of the written, oral, or performance >test? I'd go with the written test, but that's just me. >'cid Ôooh > A joke goes: a person's significant other passes away for proper and > expectable reasons. A month or so later, that person tries to use the > car to go somewhere and the car does not start. The person calls the > dealership named in car's paperwork and arranges for the car to be > transported to the dealership and the problem determined. Later, the > person receives a call from the dealership and is informed that the > only problem they could find was that the car was totally out of fuel > (in US, that is commonly called ``gas''). The person responds: > ``What's `gas?' Ô' It seems that the person's significant other had > managed all car maintenance issues---including refueling it weekly. That's a joke? I don't even see a punchline. Here's one for you: A guy walks into a bar and says ouch. Ôcid Ôooh === Subject: inital segments of partially ordered but not well-ordered sets Let X be a set and let < be a partial order on X. Let S be an intial segment of X (i.e. if xin S and y Let X be a set and let < be a partial order on X. Let S be an intial > segment of X (i.e. if xin S and y z in X such that S is of the form {x in X| x x<=z}? (X need not be well-ordered). Consider the rationals. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: inital segments of partially ordered but not well-ordered sets > Let X be a set and let < be a partial order on X. Let S be an intial > segment of X (i.e. if xin S and y z in X such that S is of the form {x in X| x x<=z}? (X need not be well-ordered). > Consider the rationals. What if I ask the order to be complete? Consider the product order of the reals. (x,y) <= (a,b) when x <= a, y <= b Let S = { x in R^2 | x <= (0,1) or x <= (1,0) } The least upper bound of S, lub S = (1,1) For S to be included in a down set of the form { x | x <= z } or { x | x < z } we find z >= lub S = (1,1) However both of those sets contains many more real pairs, (1/2,1/2) for example, than are contained in S. Even in the event the order is complete, as R^2 be, your conjecture fails, best admended by requiring order to be complete and total Hm. lub AxB = (lub A, lub B) ? === Subject: Weak topology questions Can anyone offer some hints for the following? Let B and C be Banach spaces and T:B -> C a linear transformation. 1. Prove that if T is continuous relative to the weak topologies of B and C, then T is bounded. 2. Prove that if T is continuous relative to the weak topology of B and the norm topology of C, then T(B) has finite dimension. Trevor === Subject: Re: Weak topology questions >Can anyone offer some hints for the following? >Let B and C be Banach spaces and T:B -> C a linear transformation. >1. Prove that if T is continuous relative to the weak topologies of B and >C, then T is bounded. This is immediate from the Closed Graph Theorem, if you know that. >2. Prove that if T is continuous relative to the weak topology of B and >the norm topology of C, then T(B) has finite dimension. >Trevor ************************ David C. Ullrich === Subject: Re: Weak topology questions ullrich@math.okstate.edu says... >Can anyone offer some hints for the following? >Let B and C be Banach spaces and T:B -> C a linear transformation. >1. Prove that if T is continuous relative to the weak topologies of B and >C, then T is bounded. > This is immediate from the Closed Graph Theorem, if you know that. Is this really the best tool for this? In any locally convex vector space a set is strongly bounded iff it is weakly bounded. Is not this just a case of applying this to C ? >2. Prove that if T is continuous relative to the weak topology of B and >the norm topology of C, then T(B) has finite dimension. >Trevor > ************************ > David C. Ullrich === Subject: Re: Weak topology questions >ullrich@math.okstate.edu says... > >Can anyone offer some hints for the following? > >Let B and C be Banach spaces and T:B -> C a linear transformation. > >1. Prove that if T is continuous relative to the weak topologies of B and >C, then T is bounded. > This is immediate from the Closed Graph Theorem, if you know that. >Is this really the best tool for this? >In any locally convex vector space a set is strongly bounded iff it is >weakly bounded. Is not this just a case of applying this to C ? Well, I wasn't insisting the the Closed Graph Theorem was the best tool. But why is what you suggest so much better? >2. Prove that if T is continuous relative to the weak topology of B and >the norm topology of C, then T(B) has finite dimension. > >Trevor > ************************ > David C. Ullrich ************************ David C. Ullrich === Subject: Re: Weak topology questions > Can anyone offer some hints for the following? > Let B and C be Banach spaces and T:B -> C a linear transformation. > 1. Prove that if T is continuous relative to the weak topologies of B and > C, then T is bounded. > 2. Prove that if T is continuous relative to the weak topology of B and > the norm topology of C, then T(B) has finite dimension. > Trevor I haven't looked at questions like this in a long time, so I might say something silly, but these particular questions look pretty straightforward. For (1), note that T being continuous (relative to the weak topologies) is equivalent to the property that if f : C -> k is any bounded functional then the composition f o T : B -> k remains bounded. If T is not bounded then we can find a sequence (b_1, b_2, b_3, ... ) in B such that Norm(T(b_i)) / Norm(b_i) goes to infinity as i goes to infinity. I think it ought to be possible to define a bounded functional on the subspace of C spanned by the T(b_i)'s, and then extend it to a bounded functional on all of C by the Hahn-Banach theorem, in such a way that precomposing with T gives us a non-bounded functional on B. As for (2), you should be able to show that if T(B) is infinite-dimensional then T^-1(U) is not open (where U is the unit ball centred at 0 in C). To see this, note the following two things: (a) If V is a subset of B, open in the weak topology, then V contains an Ôaffine subspace' of finite codimension (i.e. a fibre of linear map from B to a finite-dimensional vector space). (b) If T(B) is infinite dimensional then T^-1(U) does not contain any such subspace. === Subject: Re: Boosted decision trees compared to neural networks > I'm doing research comparing boosted decision trees to neural networks for > various types of predictive analyses. A boosted decision tree is an > ensemble tree created as a series of small trees that form an additive > model. I'm using the TreeBoost method of boosting to generate the decision > tree series. TreeBoost uses stochastic gradient boosting to increase the > predictive accuracy of decision tree models (see > http://www.dtreg.com/treeboost.htm). > The available publications comparing boosted trees to neural networks are > pretty limited, but the comparisons show boosted trees matching, and in some > cases exceeding, the accuracy of neural networks. This doesn't mean much unless your NNs are ensembles that may include bagging, boosting and arcing. Hope this helps. Greg > If you have data that you have successfully (or unsuccessfully) modeled > using neural networks, I would like to talk to you. I will be happy to > build a boosted decision tree for your data and send you the results so that > we can compare the decision tree model to the neural network model. > Please e-mail me at phil.sherrod Ôat' sandh.com === Subject: Re: Resistance to Change >Then what is the relationship between there being a function to >evaluate expressions and whether or not the Halting Problem is >solvable, and why? > Showing that the halting problem is not solvable is the same > as _evaluating_ the truth value of the expression the > halting problem is solvable. You're merely begging the question. How does the expression itself determine the value of the halting problem is solvable? What algorithm is it carrying out that results in the truth value of that proposition? (If you had such an expression, you wouldn't need the function (EVAL) to evaluate expressions. You could simply run the expression itself as a program. Unless of course you don't have much experience programming.) If it could merely calculate the halting problem is solvable then why couldn't it, by your reasoning, calculate the truth value of the simpler proposition program X halts? Charlie Volkstorf Cambridge, MA > ************************ > David C. Ullrich === Subject: Re: Resistance to Change >Then what is the relationship between there being a function to >evaluate expressions and whether or not the Halting Problem is >solvable, and why? > Showing that the halting problem is not solvable is the same > as _evaluating_ the truth value of the expression the > halting problem is solvable. >You're merely begging the question. How does the expression itself >determine the value of the halting problem is solvable? What >algorithm is it carrying out that results in the truth value of that >proposition? Read the paper. And the prerequisites. >(If you had such an expression, you wouldn't need the function (EVAL) >to evaluate expressions. You could simply run the expression itself >as a program. Unless of course you don't have much experience >programming.) >If it could merely calculate the halting problem is solvable then >why couldn't it, by your reasoning, calculate the truth value of the >simpler proposition program X halts? Uh, because that's not simpler? Even I can determine the truth value of the halting problem is solvable, while there does not exist an algorithm to find the truth value of X halts. >Charlie Volkstorf >Cambridge, MA > ************************ > David C. Ullrich ************************ David C. Ullrich === Subject: Re: Resistance to Change >Then what is the relationship between there being a function to >evaluate expressions and whether or not the Halting Problem is >solvable, and why? > > Showing that the halting problem is not solvable is the same > as _evaluating_ the truth value of the expression the > halting problem is solvable. > You're merely begging the question. How does the expression itself > determine the value of the halting problem is solvable? What > algorithm is it carrying out that results in the truth value of that > proposition? > (If you had such an expression, you wouldn't need the function (EVAL) > to evaluate expressions. You could simply run the expression itself > as a program. Unless of course you don't have much experience > programming.) > If it could merely calculate the halting problem is solvable then > why couldn't it, by your reasoning, calculate the truth value of the > simpler proposition program X halts? The trivial answer is that it's generally impossible to answer does program X halt?! A more detailed discussion might mention how the main Theorem in the paper takes some fictional function that answers does X halt? and proves that it is impossible (BTM). I think somebody has little understanding of what LISP actually is. If you think it's a programming language for example, you're wrong; that just happens to be one of the things it can do. === Subject: Re: Suggestion: We should have a sci.math.discrete >Shall we have a specific place to discuss problems on discrete mathematics? > Have you looked at http://mathforum.org/epigone/discretemath === Subject: Re: Suggestion: We should have a sci.math.discrete Sorry for that, I'm just a newbie in using usenet. I don't know how to add a new group at all. Perhaps I should find some tuturial on usenet to read. : ( Could someone kind help me? > huh,I wish people who have interest in discrete mathematics could > support this. > What do you mean by support? Is there a petition or form of some kind? > Finite isn't there either. I may have better l than you do, since > engineering- and computer-science forums frequently discuss such subjects. > As to Usenet groups like this one, I suppose you follow Mr. Usenet's > procedures for adding a new group. (I don't know exactly what they are.) > Then when someone is interested in discrete mathematics and types discrete > in the search for a group, they will find that it's there, and add it to > their list of subscribed groups. Eventually a critical mass of such > individuals will be reached. > Those who want to encourage specialized groups might see if there's a > specialized group that exactly matches your subject, and cross-post. === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century Okay. Einstein stood on the shoulders of giants. Tell us something we didn't know. On the other hand, there was a tiny bit in there that was worth saying: > Science, by its very nature, is insular. In general, chemists read > and write about chemistry, biologists read and write about biology, > and physicists read and write about physics. But they may all be > competing for the same research dollar (in its broadest sense). > Thus, if scientists wanted more money for themselves, they might > decide to compete unfairly. The way they can do this is convince the > funding agencies that they are more important than any other branch > of science. If the funding agencies agree, it could spell difficulty > for the remaining sciences. One way to get more money is to create a > superhero - a superhero like Einstein. Hmmmm... Einstein was a great genius of course, but there were lots of other great geniuses that nonscientists have never heard of. The above paragraph just might be an explanation of why Einstein is so much better known than von Neumann for example. -- http://hertzlinger.blogspot.com === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century Joseph Hertzlinger > Science, by its very nature, is insular. In general, chemists read > and write about chemistry, biologists read and write about biology, > and physicists read and write about physics. But they may all be > competing for the same research dollar (in its broadest sense). > Thus, if scientists wanted more money for themselves, they might > decide to compete unfairly. The way they can do this is convince the > funding agencies that they are more important than any other branch > of science. If the funding agencies agree, it could spell difficulty > for the remaining sciences. One way to get more money is to create a > superhero - a superhero like Einstein. > Hmmmm... Einstein was a great genius of course, but there were lots of > other great geniuses that nonscientists have never heard of. The above > paragraph just might be an explanation of why Einstein is so much > better known than von Neumann for example. We now return you to our regularly scheduled discussion of black helicopters and Area 51. === Subject: Re: Ubiquitous Naturals, Infinity So you have for any element of NxN the ordered pair (a, a) is zero, (a+n, a) is n, and (a, a+n) is negative n. NxN has each element of Z being represented many times, each element of NxN being a representation of an element of Z. You might consider using {}xN and Nx{}, with the ordered pair (n, {}) being n and ({}, n) being negative n, with ({},{}) being an element of either and equalling zero, {}. NxN otherwise has each element of Z being represented many times. How do you mechanically traverse NxN to subtract two from one and get a result? I think you need one external variable. You can add pairwise those ordered pairs, vector addition, and get as a result the sum of the two elements of Z they represent, (1,0)+(0,2)=(1,2)=-1. That's pretty good. Basically it's similar to a bunch of functions f(n)= -n + C, defined for C >= n. I'm glad to see you mention less than empty sets. What do you have in mind? I'm accustomed to your lack of approbation. What if you have two copies of the sets of ordinals, and apply a definition that one set is the non-negative integers and the other the non-positive integers? Let infinity equal zero or negative one, or rather, the ordinal zero negative infinity or less than any integer. That's about a relation defined for (n, 00-n), that being along the lines of (n, -n). If there are only ordinals in the model then it may be non-trivial to represent ordered pairs, which is generally done using composites in some standard models, for example {a, {a, b}} representing (a,b) and {b, {a, b}} representing (b,a). In a model where every set is an ordinal there are still those composites, they just each have a representation as an ordinal. For example {0, {0,1}} might be a von Neumann ordinal, three, you have it being negative one. Such a model might be not satisfactory. That's interesting. Please present the constructions you mention of Q and R. I'm serious. What do you call two proper classes? Is any proper class thus equal to each other, or is void just empty? Ross F. === Subject: Re: Ubiquitous Naturals, Infinity > So you have for any element of NxN the ordered pair (a, a) is zero, > (a+n, a) is n, and (a, a+n) is negative n. NxN has each element of Z > being represented many times, each element of NxN being a > representation of an element of Z. You might consider using {}xN and > Nx{}, with the ordered pair (n, {}) being n and ({}, n) being negative > n, with ({},{}) being an element of either and equalling zero, {}. > NxN otherwise has each element of Z being represented many times. As this was not of my invention, but is a standard construction, I have no power to change it. And as it works so well, I have no desire to change it. Each element of Z is represented once, by an equivalence class. If N is the zero-origin version of the naturals with {} as zero, then (n,{}) and ({},n) already represent n and -n, respectively. > How do you mechanically traverse NxN to subtract two from one and get > a result? The usual way is by defining x - y as x + (-y). Do you have a problem with that? I think you need one external variable. For what, and external to what? > You can add > pairwise those ordered pairs, vector addition, and get as a result the > sum of the two elements of Z they represent, (1,0)+(0,2)=(1,2)=-1. > That's pretty good. Basically it's similar to a bunch of functions > f(n)= -n + C, defined for C >= n. > I'm glad to see you mention less than empty sets. What do you have > in mind? It was your own suggestion that the lack of them made negatives difficult to define. About which I have just showed you to be wrong, again. I'm accustomed to your lack of approbation. You work so hard to earn it. > What if you have two copies of the sets of ordinals, and apply a > definition that one set is the non-negative integers and the other the > non-positive integers? Let infinity equal zero or negative one, or > rather, the ordinal zero negative infinity or less than any integer. > That's about a relation defined for (n, 00-n), that being along the > lines of (n, -n). What if we are just satisfied with the perfectly adequate system that we already have? > If there are only ordinals in the model then it may be non-trivial to > represent ordered pairs, which is generally done using composites in > some standard models, for example {a, {a, b}} representing (a,b) and > {b, {a, b}} representing (b,a). In a model where every set is an > ordinal there are still those composites, they just each have a > representation as an ordinal. For example {0, {0,1}} might be a von > Neumann ordinal, three, you have it being negative one. Such a model > might be not satisfactory. > That's interesting. Please present the constructions you mention of Q > and R. Please find them for yourself. === Subject: PROOF that emulators are impossible boundary=----=_NextPart_000_000E_01C42DF5.097645C0 ------------------------------------------------------------- -------- charset=iso-8859-1 Assume an emulator exists, call it UTM, and a suitable godel numbering is found for all programs (TMs) that can be parsed by the UTM. Each TM parses its own 1 parameter, TMt is the TM with godel number t. TMt(p) = a <==> UTM(t, p) = a ......(1) Now construct a function that emulates a given function and adds 1 to the result. The parameter of the given function will be its own godel number. function ADD(t) ( return UTM(t, t) + 1 ) If g is the godel number of ADD, what is the value of ADD(g)? ADD(g) = UTM(g,g) + 1 = ADD(g) + 1 .......from (1) = UTM(g,g) + 1 + 1 = ADD(g) +1 + 1 = UTM(g,g) + 1 + 1 + 1 ADD does not terminate, this contradicts the assumption that a function emulator is possible. Herc -- oo |mn / / / / - Herc, The Unrecognised Truman / K-9/ / / - Join www.chatty.net - / / - Nanotechnology is gonna be HUGE... (RMF) ------------------ === Subject: Re: PROOF that emulators are impossible > Assume an emulator exists, call it UTM, and a suitable godel numbering > is found for all programs (TMs) that can be parsed by the UTM. > Each TM parses its own 1 parameter, TMt is the TM with godel number t. > *TMt(p) = a <==> UTM(t, p) = a ......(1)* > Now construct a function that emulates a given function > and adds 1 to the result. The parameter of the given function > will be its own godel number. > *function ADD(t) (* > * return UTM(t, t) + 1* > *)* Nitpick: ADD emulates a given TM with it's godel number as input and adds one. ADD is a TM. > If g is the godel number of ADD, what is the value of ADD(g)? > *ADD(g) = UTM(g,g) + 1* > *= ADD(g) + 1 .......from (1)* > *= UTM(g,g) + 1 + 1* > *= ADD(g) +1 + 1* > *= UTM(g,g) + 1 + 1 + 1* > ADD does not terminate, this contradicts the assumption that a function > emulator > is possible. No, since there is nothing that says any given TM must halt. Also, UTM is not a function emulator, it is a TM emulator. Finally, if by function you mean a turing computable function for all inputs, all you have shown is that ADD is not turing computable for all inputs. When you do something like this, make sure you identify all your assumptions. In this case you had a few, including that ADD was a function (whatever you mean by that). -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: PROOF that emulators are impossible > Now construct a function that emulates a given function > and adds 1 to the result. The parameter of the given function > will be its own godel number. > function ADD(t) ( > return UTM(t, t) + 1 > If g is the godel number of ADD, what is the value of ADD(g)? > ADD(g) = UTM(g,g) + 1 > = ADD(g) + 1 .......from (1) > = UTM(g,g) + 1 + 1 > = ADD(g) +1 + 1 > = UTM(g,g) + 1 + 1 + 1 > ADD does not terminate, this contradicts the assumption that a > function emulator is possible. ADD(g) does not halt, so UTM(g,g) does not halt as well. I don't see a contradiction - the emulator works perfectly. Michael -- Feel the stare of my burning hamster and stop smoking! === Subject: Are there any non-gifted scientists?!?!? I'm a high school student, about to go to college to study math and/or computer science. I'm basically a nerd, been interested in programming for a while but looking back I had a pretty distorted view of what programming actually was when I was hacking away at code in elementary school and middle school (I'm sure plenty of you had similar experiences). More recently I've picked up math as a hobby and become more of a science nerd than a computer nerd. Here's my dilemma: I ain't that smart. Failed my school's gifted test each time I took it, usually score in the 120s on online IQ tests (except a 150 on the obviously rigged iqtest.com test). That alone wouldn't be a tragedy, except for the fact that my high school grades are pretty average... at least for an honors kid. This year, schoolwork has become my *obsession*, and while my grades improved from B's and C's to A's and B's, these weren't quite the grades I was looking for, especially considering my courseload is rather light. Given, I'm not going to become an outstanding student overnight. Most students I'm competing with have been working hard since elementary school, so I should expect to have to work much harder than them to obtain similar grades until I catch up. But the problem is that I may never truly catch up, especially if I'm taking difficult classes with really bright kids in college, because I may simply not have the intellectual ability. Talent in math and the sciences exists, it certainly isn't completely accounted for by IQ but I'm sure IQ plays a large role in it. I've met a lot of people with similar intellectual interests as I do and read many a usenet IQ debate among such people, and I've yet to encounter a person successful in mathematics or a hard science who does not have a great deal of talent in the subject. This usually means IQ > 130. Here are a few interesting figures that someone will probably bring up: - Richard Feynman's IQ was 125. James Gleick's biography, page 30: Still, his score on the school IQ test was a merely respectable 125. I'd wager this result was some sort of ßuke, but regardless of his IQ per se, it's clear that from a young age Feynman had a considerable amount of talent in math and science. Unfortunately that cannot be said of an IQ-120-something person such as myself. - The average IQ of a Nobel Prize winner (not sure whether this is in any field or in the physical sciences) is somewhere in the 120 range. I heard this from the Test The Nation televised IQ test (which I did and got a 123 on, although the actual score would be a bit higher given it started at age 18). Anyway, I've done some research and never found where this statistic actually comes from. Can anyone enlighten me? As has often been said to me and as I'm sure many of you folks will advise, it's all about hard work. But even if I could force myself to work twice as hard as everyone else and get the grades and coursework necessary to go to grad school, what do I do next when the work becomes even more challenging? I value education. In fact, being non-gifted gives me even more of a reason to value education... so I can work toward reaching my true potential (albeit a somewhat limited potential). Why should I work my ass off studying something that comes easy to others, when I could just go into something less... intellectual demanding. Speaking of certain intellectual demands, would I be better off choosing a different scientific field? Maybe my IQ would prevent me from being a mathematician, but how about something like, say, psychology? Maybe that's a bad example... would anyone care to offer a list of low-IQ fields? Why should I be interested in math and science in the first place? It seems that most people with average IQs (say, within 1 s.d. from the mean) have little or no qualms about being average. They're more concerned with earthly things, such as their appareance, crappy music, television, etc. I like to think that I've elevated myself from this. Not that I'm any better than these people, just that I'm not a materialist. I've made the pursuit of knowledge the most important pursuit in my life, because knowledge combats ignorance. Knowledge is our criteria for evaluating new knowledge, for making decisions and setting priorities. I've chosen to study math and science namely because I'm fascinated by these subjects. But additionally, I often think to myself that I won't have a better opportunity than now to gain an understanding of these subjects. My dad is in his forties and can't have more than a middle school understanding of math. There's nothing stopping me from switching to some liberal arts major, placing out of calculus, and taking the minimum number of science electives via xxxx for non-majors courses. But what would I think of that decision when *I'm* 40? I could pick up a graduate level psychology paper right now and comprehend a pretty good deal of it. But give me or just about any other (sane) human being a paper on the topology of k-manifolds [insert more geordi-from-star-trek-talk here] and there's no way in Hell I'll comprehend a bit of it. At the same time, I wonder if I'm going to be wasting arguably the best years of my life studying the stuff. I guess the big issue for me is *how much* commitment I want to put into it. Obviously I need to keep my life balanced with other interests and reserve some time for fun no matter what I decide to do. Wow I've spent a lot of time writing this post. Anyway, I'd be really interested in your replies. I'm particularly interested in knowing if there is anyone reading this who is/was in a similar situation as I am. And referring back to the subject text, I'm wondering if anyone can name some names. Name me a few respected mathematicians, computer scientists, physicists, any field will work actually, who are not gifted. I better be getting to bed... === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. You are overestimating the bulk. Welcome in the reality of the overestimated. Being gifted is one thing and finding the right spot where the talent can be used is quite another. And getting the right estimation by the surrounding is another story. And even if the above three are optimal it doesn't automatically mean to become rich either. Rene -- Ing.Buero R.Tschaggelar - http://www.ibrtses.com & commercial newsgroups - http://www.talkto.net === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. Math and programming overlap on a regular basis. They often complement each other. [IQ stuff snipped] Don't worry about IQ, it's over-rated. Worry about what you enjoy, and work at it. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? Believe it or not, knowing how to work early makes a difference. Sooner or later everyone stops coasting and has to work. Not everyone makes the adjustment well. If you know how to study effectively, you can push forward. Also, understand that not everyone needs to go to grad school. The first concern should be getting the education to meet your goals. What are they? > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. Because it's fun. I enjoy math and programming. That's why I studied math in school, and am studying programming now. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? As I said before, don't worry about IQ. If you know how to study, and when to get help, you can learn what you need to. Attitude is more important than intelligence from what I've seen. [value of knowledge snipped, though good] Basically, you understand that education has value. Why would you want to limit yourself just because it might be hard? Go for whatever you want to learn, and don't worry about ability until no amount of work or assistance gets to understanding. -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: Are there any non-gifted scientists?!?!? There are many ways to enhance your thinking. Working with visualizations is a good way. Some have problems with that but everyone can get better. I am sure there are lots of reading material out there === Subject: Re: Are there any non-gifted scientists?!?!? >I'm a high school student, about to go to college to study math and/or >computer science. I'm basically a nerd, been interested in >programming for a while but looking back I had a pretty distorted view >of what programming actually was when I was hacking away at code in >elementary school and middle school (I'm sure plenty of you had >similar experiences). More recently I've picked up math as a hobby >and become more of a science nerd than a computer nerd. >Here's my dilemma: I ain't that smart. Failed my school's gifted test >each time I took it, usually score in the 120s on online IQ tests >(except a 150 on the obviously rigged iqtest.com test). That alone >wouldn't be a tragedy, except for the fact that my high school grades >are pretty average... at least for an honors kid. This year, >schoolwork has become my *obsession*, and while my grades improved >from B's and C's to A's and B's, these weren't quite the grades I was >looking for, especially considering my courseload is rather light. >Given, I'm not going to become an outstanding student overnight. Most >students I'm competing with have been working hard since elementary >school, so I should expect to have to work much harder than them to >obtain similar grades until I catch up. But the problem is that I >may never truly catch up, especially if I'm taking difficult classes >with really bright kids in college, because I may simply not have the >intellectual ability. Talent in math and the sciences exists, it >certainly isn't completely accounted for by IQ but I'm sure IQ plays a >large role in it. >I've met a lot of people with similar intellectual interests as I do >and read many a usenet IQ debate among such people, and I've yet to >encounter a person successful in mathematics or a hard science who >does not have a great deal of talent in the subject. This usually >means IQ > 130. I have no idea what my IQ is. I was never especially good at math. In college calculus I got B's and C's, managed to get a D in an advanced calculus course. I'm finishing up the research for my Ph.D. in physics. A friend of mine said that unlike me, he just doesn't have a math gene. I asked him how much work he's put into it lately. I felt like the endless hours I'd spent on homework, and just using it in physics classes, was dismissed as talent; if you've got it, you've got no problems. I don't think I could be a theorist, but I can certainly spin a wrench. The typical set of college courses prepares you to be a theorist, the experimentalist needs a whole set of skills that are mostly learned on the job. Combine physics and programming -- computational physics. Numerical work is widespread and important in both sciences and engineering. Everyone treats the DAQ man well, because otherwise someone else will have to make the computer work right. When you still have some classes left to take, start looking at the job market in your geographical area of interest, find out what employers are looking for when you still have time to add those skills. To be prepared is more important than to simply be smart. -- What are the possibilities of small but movable machines? They may or may not be useful, but they surely would be fun to make. -- Richard P. Feynman, 1959 === Subject: Re: Are there any non-gifted scientists?!?!? > [...] > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > [...] I bet most mathematicians and scientists have never had their IQ measured. And why would they? It isn't an important thing, though you seem to be obsessed with it. -- G.C. === Subject: Re: Are there any non-gifted scientists?!?!? > Here's my dilemma: I ain't that smart. Don't sweat it, as long as you're willing to work hard for what you want. I'm currently dating a lady who's an experimentalist in neurobiology. She's a published expert in neurotransmitters. She's smart, but isn't exceptional as far as her innate intelligence is concerned. She's just dedicated, and has made a carreer for herself. My advice to you is to work hard and go for it. -Mark Martin === Subject: Re: Are there any non-gifted scientists?!?!? > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. Traditional SAT/10 = IQ. Minimum IQ for college (with academic qualification) is 110 (SAT 1100). 120 IQ will fully qualify you for PhD work in anything but science. ~120 is entry fee for PhD work in descriptive sciences. The ones that bear on heavy mathematics will need more. Even American zero goal education misses destroying enough functional mentalities that MIT and Caltech have full entering classes. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. Intelligence is the ability to succeed in novel situations. Do what you can do, do what you enjoy. Social and financial security lay in being a parasite not a producer - manager, lawyer, politician, advocate, priest. Able scientists are fanatics. They are expressing passion. If you are merely expressing hard work you will be crushed by graduate school in the sciences. It is not a place for sanity. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. ~130 for physics is a good start. A professional mathematician should start around 170 IQ. I know faculty who was a child math prodigy. She saw in a second what took me four sweated days to reproduce after knowing it was there. It was an awesome performance of hardwired genius; it was SOP for her. I've done the same to people in chemistry, repeatedly. You can compete with innate talent here and there, but not in the long run. Genius is a trump card. Societies who cherish their wounded over their Gifted wither and die. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. That's not really true. Feynman took pride in being a boor. His verbal scores were purposefully awful. Look, the guy got 5 of 5 in the Putnam competition and went home from the test early. It is not unusual for the Putnam competition median score to be ZERO - the most common score is ZERO. Virulently anti-Semitic Harvard dropped trou and spread for Feynman. He told Harvard to go to Hell, and proceeded to bother Princeton. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. Again, this is not meaningful. IQ tests seek to assay a broad range of abilities. This is fine for Type I genius - the result of talent plus hard work. The wild mentalties, the Severely and Profoundly Gifted, are where the real action is. Type II genius is the wild and hairy ride where seeing the answer doesn't make it any clearer. Being a sledgehammer is very nice for whacking things in general. If you want deep holes punched, you need an ice pick - very narrow, very focused, and thrust with a supernova. Shaped charges do damage incredibly beyond their apparent expended effort. Space them out another foot and nothing much happens. Anybody can do one incredible thing (obvious exceptions noted by demonstration in sci.physics - idiots are worthless except as meat). That does not a career make. You have to fill 30-40 years. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. Hard work will allow you to play the piano or the violin. A prodigy is born with perfect pitch and innate talent. Your best efforts cannot begin to compete with the original package contents. Compete where you can win. There is no divine imprimatur associated with talent. Julliard is filled with people who will starve or play background for squealing slumbunnies dripping gold bling bling. Go to a piano. Hit only the black keys, at random. Sounds nice, yes? That doesn't make you Mozart. OK to diddle at home, not so good in a concert hall (even if you are John Cage). Jackson Jack the Dripper Pollack was a talentless house painter. He was a great salesman, he knew the territory, and his value to his patrons included his early death. (In the beginning he made some effort with his work. Toward the end there were no delusions and all he did was toss paint. You can use metallographic software or whatever to chart the fractal dimension of his work. Early on he fit together areas. At the end it was random splatter, $/area covered.) > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. Do what you want and enjoy. Wander through a university library and see what turns you on. UC/Irvine has 1200 technical perodicals stacked in its rotunda. Heaven! - but not if you *have* to read the whole horseshoe very month. I personally have a mild fetish for growing crystals. It doesn't extend to daily production of single crystal silicon 35 cm in diameter and five feet long. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? Do what you want. IQ is not a meaningful threshhold, merely a convenience. Windows' Hearts is a dishonest game. It can therefore be beaten with good success. Interesting for an hour but not for a lifetime. Nothing says you cannot have a day job for money and a hobby in your garage (aside from Homeland Severity, the War on Drugs, the EPA, Haz-Mat, OSHA...). Be an enforcer. A cop with a high school GED makes about three times the Official salary of an NIH Fellow - more than four times including benefits and bribes. > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. Nah. Join Mensa, look around. The Gifted are generally unpleasant people, even amongst themselves. You don't hire them as drinking buddies, you hire them as hit men. Forced social situations like tenured academia then get veeeery interesting. [snp] > I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. If you can find anything of value in it, publish a paper. > But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. Mathematics is objective. If you want a working cell phone, truth is brutal and uncompromising. Everything in the social sciences is both true and untrue. A society managed by posseurs will be ed to Hell, as we are, http://www.mazepath.com/uncleal/comprom.htm > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. Yes. Do things in your youth you can fondly regret in your old age. Starting with a registered nurse is really good. Damn! > I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. NOT QUALIFIED! Really. You'll be much happier doing what makes you happy. Screw external approval. Do what pleases you. You can always get a shotgun or sword and disapprove back - for a price. > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... I imagine that there are 5'8 basketball players. Showing up 7' tall has its advantages. 58' is no diadvantage in hockey. Pray that you don't meet a Wayne Gretsky on the other team - and remember that the coach gets paid win or lose, and need have no hockey abilities on the ice whatsoever. -- Uncle Al http://www.mazepath.com/uncleal/qz.pdf http://www.mazepath.com/uncleal/eotvos.htm (Do something naughty to physics) === Subject: Re: Are there any non-gifted scientists?!?!? Yours is a thoughful post. The short answer to your question Are there any non-gifted scientists? is yes, most of them. Most scientists, even those with Phd awards, are engaged in research, teaching or other work that requires a fairly strong intellectual prowess, but no special Ôgift' in the sense we attribute to those exceptionally high achieving scientists (Einstein being obvious, but there are many many). Do not feel put off at the prospect of not being the next Einstein, your peers aren't either. Now to some points > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. Drop the Ônerd' label, you don't need labels. If you end up a scientist you'll be a scientist. Just sharing my opinion of the whole geek/nerd label thing, don't play the label game. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. You've shown that you're tenacious and work hard, already you're out in front. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. In a very broad general sense IQ is reportedly related to capability in various intellectual fields, it's also a very blunt measure so don't place emphasis on it. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? Just another example Niels Bohr, a nobel prize winning physicist of the early 20th century was said to be a slow but doggedly determined thinker, apparently even needing movie plots explained to him, and taking good time to understand the things he studied. Yet he was so good a what he did that he became a focal point for most noted physicists of the time (literally, at his institute in denmark). Great quotation from him; never express yourself more clearly than you can think There are all kinds of examples of brilliance coming out from people who may not immediately appear Ôgifted' in the sense we generally mean. > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. Because you *know* it matters and even if you're no Einstein (or indeed no Bohr) you can still make a difference, a positive contribution to mankind. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? Whatever you choose will require some intellectual capacity, chemistry, geology - no matter what - they all deal in abstractions and require rigorous thinking. It ßoors me the way the most brilliant people can ßit around different areas of their subjects, even different subjects, and just add so much, more than the average colleague's life's work. Poeple like Feynman, Penrose and so on. but for each of those there are thousands of good scientists making a real difference without which the much heralded Ôgifted ones' would be occasional blips on a sparse field of human knowledge. Don't compare yourself with those rarest folks, you'd be setting yourself up for feeling inadaquate when really you're not at all. Of possible interest to comp.programming, John Kemmeny (co inventor of the computer langauge BASIC) spent some time as Einstein's mathematics assistant, quoting from Kemmeny Einstein did not need help in physics. But contrary to popular belief, Einstein did need help in mathematics. So Einstein himself was good but not so good he couldn't use some help. > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I think you've answered your own question here! > I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. Learning these things while young is advantageous. There are few scientists studying for their PhD when in their thirties or forties compared to younger folks in their twenties, not necessarily for lack of intellect but for practicalities of the commitments you make as you get older and the opportunities you end up having to close the door on. If i had my youth again i would go through a far more rigerous route of science and mathematics. if i knew then what i know now, that kind of thing! > There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. That's because such papers are built upon layer after layer of foundation knowledge, which needs to be gained *before* tackling those areas, while less technical work (no less valuable) draws from concepts more ingrained in our understanding of language and meaning as we grow up and so (on the surface) more accesable to any given reader. I'd double check if your *really* do understand what's being developed in those psyhology papers in terms of their implications and models of the mind they are suggesting, there's likely more depth there than you may at first see. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. If you enjoy the journey then it'll not be wasted and will likely leave you a more knowledgeable and better thinker with more options as to the remainder of your life. > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... Hope this reply is of some help to you, to be honest i'm somewhat envious of your position and the insight you have at your point in life. You're reallt thinking this through and seeking input, that's a good start. === Subject: Re: Are there any non-gifted scientists?!?!? For your question if there are any non gifted scientists. Yes, ask uncle Al or what hes called. :) Der Fugue skrev i meddelandet >I'm a high school student, about to go to college to study math and/or >computer science. I'm basically a nerd, been interested in >programming for a while but looking back I had a pretty distorted view >of what programming actually was when I was hacking away at code in >elementary school and middle school (I'm sure plenty of you had >similar experiences). More recently I've picked up math as a hobby >and become more of a science nerd than a computer nerd. >Here's my dilemma: I ain't that smart. Failed my school's gifted test >each time I took it, usually score in the 120s on online IQ tests >(except a 150 on the obviously rigged iqtest.com test). That alone >wouldn't be a tragedy, except for the fact that my high school grades >are pretty average... at least for an honors kid. This year, >schoolwork has become my *obsession*, and while my grades improved >from B's and C's to A's and B's, these weren't quite the grades I was >looking for, especially considering my courseload is rather light. >Given, I'm not going to become an outstanding student overnight. Most >students I'm competing with have been working hard since elementary >school, so I should expect to have to work much harder than them to >obtain similar grades until I catch up. But the problem is that I >may never truly catch up, especially if I'm taking difficult classes >with really bright kids in college, because I may simply not have the >intellectual ability. Talent in math and the sciences exists, it >certainly isn't completely accounted for by IQ but I'm sure IQ plays a >large role in it. >I've met a lot of people with similar intellectual interests as I do >and read many a usenet IQ debate among such people, and I've yet to >encounter a person successful in mathematics or a hard science who >does not have a great deal of talent in the subject. This usually >means IQ > 130. >Here are a few interesting figures that someone will probably bring >up: >- Richard Feynman's IQ was 125. James Gleick's biography, page 30: >Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his >IQ per se, it's clear that from a young age Feynman had a considerable >amount of talent in math and science. Unfortunately that cannot be >said of an IQ-120-something person such as myself. >- The average IQ of a Nobel Prize winner (not sure whether this is in >any field or in the physical sciences) is somewhere in the 120 >range. I heard this from the Test The Nation televised IQ test >(which I did and got a 123 on, although the actual score would be a >bit higher given it started at age 18). Anyway, I've done some >research and never found where this statistic actually comes from. >Can anyone enlighten me? >As has often been said to me and as I'm sure many of you folks will >advise, it's all about hard work. But even if I could force myself to >work twice as hard as everyone else and get the grades and coursework >necessary to go to grad school, what do I do next when the work >becomes even more challenging? >I value education. In fact, being non-gifted gives me even more of a >reason to value education... so I can work toward reaching my true >potential (albeit a somewhat limited potential). Why should I work my >ass off studying something that comes easy to others, when I could >just go into something less... intellectual demanding. >Speaking of certain intellectual demands, would I be better off >choosing a different scientific field? Maybe my IQ would prevent me >from being a mathematician, but how about something like, say, >psychology? Maybe that's a bad example... would anyone care to offer >a list of low-IQ fields? >Why should I be interested in math and science in the first place? It >seems that most people with average IQs (say, within 1 s.d. from the >mean) have little or no qualms about being average. They're more >concerned with earthly things, such as their appareance, crappy music, >television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a >materialist. I've made the pursuit of knowledge the most important >pursuit in my life, because knowledge combats ignorance. Knowledge is >our criteria for evaluating new knowledge, for making decisions and >setting priorities. I've chosen to study math and science namely >because I'm fascinated by these subjects. But additionally, I often >think to myself that I won't have a better opportunity than now to >gain an understanding of these subjects. My dad is in his forties and >can't have more than a middle school understanding of math. There's >nothing stopping me from switching to some liberal arts major, placing >out of calculus, and taking the minimum number of science electives >via xxxx for non-majors courses. But what would I think of that >decision when *I'm* 40? I could pick up a graduate level psychology >paper right now and comprehend a pretty good deal of it. But give me >or just about any other (sane) human being a paper on the topology of >k-manifolds [insert more geordi-from-star-trek-talk here] and there's >no way in Hell I'll comprehend a bit of it. >At the same time, I wonder if I'm going to be wasting arguably the >best years of my life studying the stuff. I guess the big issue for >me is *how much* commitment I want to put into it. Obviously I need >to keep my life balanced with other interests and reserve some time >for fun no matter what I decide to do. >Wow I've spent a lot of time writing this post. Anyway, I'd be really >interested in your replies. I'm particularly interested in knowing if >there is anyone reading this who is/was in a similar situation as I >am. And referring back to the subject text, I'm wondering if anyone >can name some names. Name me a few respected mathematicians, computer >scientists, physicists, any field will work actually, who are not >gifted. >I better be getting to bed... === Subject: Re: Are there any non-gifted scientists?!?!? Well its more important to know allot about your field then being smart. Sure if you are smart and maths is your cup of tea you will breaze through it all. But a funny thing in maths is that oftern its the mistakes you make that tell you more and may even inspire you to go off and prove something. Problem is most smart people dont make allot of mistakes. As a side not didnt one of the conjectures surrounding FLT shown from someone making abit of a mistake that lead to a very interesting end? Btw i dont think i knew much maths until i got to uni where i have worked really hard on it to get where i am now. But even now i dont feel as if i know much maths at all. There is just too much of it. stephen === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. Do programming. I know a guy who graduated just over a year ago from comp. sci. and makes 45% more than the Physics Professors at the institution he attended (fairly respectable for his field of study) and 25% more than his comp. sci professors. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). The true result of an IQ test is if the subject comes out understanding that IQ tests are useless, obviously. > That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. Again, these grades only serve to get you beaurocratically certified and admitted into an institution of higher education - don't expect to learn anything there, it's just another expensive level or beaurocratic certification (an expensive day care centre). > This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. That guy had the same problem you refer to, his strategy was to 1. Get industry experience. 2. Take the initiative and learn _USEFUL_ skills (not the crap they teach). and the strategy succeeded with astonishing success. I can vouch for that! > But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. This guy almost got fired from his place of work because some of his colleagues (who graduated from some from the most prestigous technical colleges on this planet) were pissed off at his remuneration package - they had 5-8 years exp and he just 1. So much for being gifted. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. That's all crap. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? Crap. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... Your obsession with IQ's is a reßection of your unfounded faith in the system. ALMOST ALL academic fields (medical, some science, political, religious, political) are USELESS BEAUROCRACIES. Once you understand that, then all your concerns will be addressed. === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). > The true result of an IQ test is if the subject comes out > understanding that IQ tests are useless, obviously. > That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. > Again, these grades only serve to get you beaurocratically certified > and admitted into an institution of higher education - don't expect > to learn anything there, it's just another expensive level or > beaurocratic certification (an expensive day care centre). > This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. > That guy had the same problem you refer to, his strategy was to > 1. Get industry experience. > 2. Take the initiative and learn _USEFUL_ skills (not the crap they > teach). Whoa... they teach crap? As someone else pointed out, it does depend on the quality of the individual school. Not everything you learn is going to be directly applicable to the real world, and I can't help but think that's a good thing. Highly competitive schools with outstanding reputations put much more emphasis on the theoretical than on directly applicable job skills. It's at the tech schools and community colleges that you learn how to use Word and Excel and maybe a bit of Java. Look at CMU, UIUC, etc... these schools have CS programs immersed in theory. Over the next several decades programming languages will fade in and out of popularity, and if you've spent every waking moment of your life working at C++, where will you be when something else comes along and replaces it? The concepts taught in a solid CS curriculum will still be valued in such a situation, but not just for programming... the student will also have a solid knowledge of mathematics, some physics and other sciences, and such knowledge will enrich the student's life even if (s)he ends up cleaning toilets at McDonald's for a living. At least that's my rationale for wanting to put myself through 4(+?) years of prolonged sleep deprivation... > and the strategy succeeded with astonishing success. I can vouch for > that! > But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. > This guy almost got fired from his place of work because some of his > colleagues (who graduated from some from the most prestigous technical > colleges on this planet) were pissed off at his remuneration package - > they had 5-8 years exp and he just 1. So much for being gifted. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > That's all crap. Could you please offer me some counterexamples then? > > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? > Crap. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. > > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? > > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. > > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > > I better be getting to bed... > Your obsession with IQ's is a reßection of your unfounded faith in > the system. obsession with IQ's... fair enough. But you have to realize that there's a reason for it. If I had my way I'd be a professional mathematician, so please offer an example of a mathematician with an IQ < 130. I've pretty much given up on that goal, but I'd still love to be a computer *scientist*. Seems like you have to be pretty bright to do that too, however. > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Once you understand > that, then all your concerns will be addressed. === Subject: Re: Are there any non-gifted scientists?!?!? > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. > Again, these grades only serve to get you beaurocratically certified > and admitted into an institution of higher education - don't expect > to learn anything there, it's just another expensive level or > beaurocratic certification (an expensive day care centre). > That guy had the same problem you refer to, his strategy was to > 1. Get industry experience. > 2. Take the initiative and learn _USEFUL_ skills (not the crap they > teach). > Your obsession with IQ's is a reßection of your unfounded faith in > the system. > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Once you understand > that, then all your concerns will be addressed. Did you not read the original poster's main concerns and motivations? He wants to become educated and enlightened... he wasn't saying that he's concerned about his job prospects and how much money he could possibly make with his education. Newsßash: not everyone cares about money, and universities are not meant to be job-training facilities. J === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. I had a friend get out of programming to go into plumbing. New construction. He makes more than all the above. And he likes his cushy job. It keeps him busy. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). > The true result of an IQ test is if the subject comes out > understanding that IQ tests are useless, obviously. On the contrary, IQ tests are very valuable. > That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. > Again, these grades only serve to get you beaurocratically certified > and admitted into an institution of higher education - don't expect > to learn anything there, it's just another expensive level or > beaurocratic certification (an expensive day care centre). Youre starting to sound like one who never graduated. > This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. > That guy had the same problem you refer to, his strategy was to > 1. Get industry experience. > 2. Take the initiative and learn _USEFUL_ skills (not the crap they > teach). > and the strategy succeeded with astonishing success. I can vouch for > that! > But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. > This guy almost got fired from his place of work because some of his > colleagues (who graduated from some from the most prestigous technical > colleges on this planet) were pissed off at his remuneration package - > they had 5-8 years exp and he just 1. So much for being gifted. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > That's all crap. I would tend to agree with this young mans conclusion. Hard work cant make up for something thats simply not there. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? > Crap. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... > Your obsession with IQ's is a reßection of your unfounded faith in > the system. > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Once you understand > that, then all your concerns will be addressed. Your comments are so far afield as to be entirely worthless. Why did you even bother? Rob === Subject: Re: Are there any non-gifted scientists?!?!? charset=iso-8859-7 Rob Duncan .8d.98.87.8b.8c .97.99.95 .92.86.94.9d.92.87 > I would tend to agree with this young mans conclusion. Hard work cant make > up for something thats simply not there. It can. The boundary is not a Julia set. What's there and what's not there is a grey area. Until one can define what needs to be there, I am not convinced that IQ matters at all, unless it's below a certain natural threshold, which is be used to delimit the idiots from the minimal functioning ones. > Rob -- Ioannis Galidakis http://users.forthnet.gr/ath/jgal/ ------------------------------------------ Eventually, _everything_ is understandable === Subject: Re: Are there any non-gifted scientists?!?!? > The true result of an IQ test is if the subject comes out > understanding that IQ tests are useless, obviously. Hey Schoenfeld, we are better than you are as you so ferverently and voluminously demonstrate across a wide range of your fugent incapabilities. It is not merely that you are ignorant. You cannot be educated. You are stooopid. The little people are forever whining that they are just as good - better! - than those with talent. Go to a library, to Dissertation Abstracts. DA/Physical Sciences fits on a couple of shelves. DA/Liberal Arts covers an entire wall - ten feet wide and high. There is one other difference: DA/Physical Sciences contains something of value. If DA/Liberal Arts'contents never existed, the world would be no different. Shoenfeld's Rule: Enough gathered in one place becomes something of value. Uncle Al's Corollary: Only to dung beetles. Hey stooopid, we can hire India to program for 1/5 the cost of Americans. Scut labor always falls to wogs and then robotics. When was the last time you pushed a slide rule, git, or did a linear least squares fit by hand? Ran anything other than a CNC lathe? gnuplot has an incredible non-linear fits package - just about any fitting function you can write on a line - and with incredibly fast execution. It's freeware, fool. OTOH... Marquardt and Levenberg, who discovered the algorithm that makes non-linear fast fits possible, were really hot stuff. -- Uncle Al http://www.mazepath.com/uncleal/qz.pdf http://www.mazepath.com/uncleal/eotvos.htm (Do something naughty to physics) === Subject: Re: Are there any non-gifted scientists?!?!? [nothing] Hey Al, tell us again how the first time derivative of distance is velocity (Ha Ha Ha). Stupid Al pointed his solar panels at the moon and then wondered why his dishes broke on the spin cycle. === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. If you have a 120 IQ and you get into a TOP comp sci school, you are probably a dead d unless you don't need sleep. Just for an intro, go to http://www-2.cs.cmu.edu/~15251/ and click on Ôcalendar' at the top. There you will find this semester's version of Great Theoretical Ideas in Computer Science It's sort of a desultory intro to many ideas germaine to comp sci. (It's a popular, fun class with a magic trick at the beginning of each lecture, though this may be hard to see on the videos.) It is a 200-level course with two very low-level prereqs and is taken mainly by freshman. Read a couple of lectures (ppt) or watch the videos and then try a homework or two. (The first is probably a gimme.) If you find the homeworks very hard or impossible, you are probably screwed for comp sci. Things get much tougher and far more time consuming from here. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). > The true result of an IQ test is if the subject comes out > understanding that IQ tests are useless, obviously. You can't tell the difference between an IQ 100 person and an IQ 160? Please. IQ tests may only give coarse classification, but they are not devoid of info. > That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. > Again, these grades only serve to get you beaurocratically certified > and admitted into an institution of higher education - don't expect > to learn anything there, it's just another expensive level or > beaurocratic certification (an expensive day care centre). Did you go to a bad school or something? Top schools teach. Of course, they are very selective. > This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. > That guy had the same problem you refer to, his strategy was to > 1. Get industry experience. > 2. Take the initiative and learn _USEFUL_ skills (not the crap they > teach). > and the strategy succeeded with astonishing success. I can vouch for > that! > But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. > This guy almost got fired from his place of work because some of his > colleagues (who graduated from some from the most prestigous technical > colleges on this planet) were pissed off at his remuneration package - > they had 5-8 years exp and he just 1. So much for being gifted. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > That's all crap. Find a counterexample. Happy hunting. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? > Crap. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... > Your obsession with IQ's is a reßection of your unfounded faith in > the system. > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Once you understand > that, then all your concerns will be addressed. Those fields are totally off topic for this discussion. Are you under the impression that advances in math come from Walmart? Slainte, Fletch === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. > If you have a 120 IQ and you get into a TOP comp sci school, you are > probably a dead d unless you don't need sleep. The school I'm planning on attending is in the top 10. Unfortunately (or maybe fortunately), I didn't get into their special honors CS program (I could transfer into it, though). Which brings me to a slightly unrelated question... how important is it to be in honors classes and programs, for grad schools and jobs and such? If the school already has a good reputation and I get an outstanding GPA without honors of any sort, is that enough? I'd suppose it's at least better than doing poorly in such classes. As for the sleep comment... unfortunately I need a pretty good deal of it to function adequately, which puts me at an additional disadvantage. The very best of the best are both brilliant and don't sleep much... the last two valedictorians at my high school averaged 4 hours of sleep a night. One strategy I'm seriously planning on implementing is this: I'm going to try to study wayy ahead of the curriculum in math and CS and hopefully gain a pretty solid knowledge of the courses I'll be taking *before* I ever actually take them. Maybe it's overkill, though. > Just for an intro, go to http://www-2.cs.cmu.edu/~15251/ and click on > Ôcalendar' at the top. There you will find this semester's version of > Great Theoretical Ideas in Computer Science It's sort of a desultory > intro to many ideas germaine to comp sci. (It's a popular, fun class with a > magic trick at the beginning of each lecture, though this may be hard to see > on the videos.) It is a 200-level course with two very low-level prereqs > and is taken mainly by freshman. Read a couple of lectures (ppt) or watch > the videos and then try a homework or two. (The first is probably a gimme.) > If you find the homeworks very hard or impossible, you are probably screwed > for comp sci. Things get much tougher and far more time consuming from > here. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). > The true result of an IQ test is if the subject comes out > understanding that IQ tests are useless, obviously. > You can't tell the difference between an IQ 100 person and an IQ 160? > Please. IQ tests may only give coarse classification, but they are not > devoid of info. > That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. > Again, these grades only serve to get you beaurocratically certified > and admitted into an institution of higher education - don't expect > to learn anything there, it's just another expensive level or > beaurocratic certification (an expensive day care centre). > Did you go to a bad school or something? Top schools teach. Of course, > they are very selective. > This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. > Given, I'm not going to become an outstanding student overnight. Most > students I'm competing with have been working hard since elementary > school, so I should expect to have to work much harder than them to > obtain similar grades until I catch up. > That guy had the same problem you refer to, his strategy was to > 1. Get industry experience. > 2. Take the initiative and learn _USEFUL_ skills (not the crap they > teach). > and the strategy succeeded with astonishing success. I can vouch for > that! > But the problem is that I > may never truly catch up, especially if I'm taking difficult classes > with really bright kids in college, because I may simply not have the > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. > This guy almost got fired from his place of work because some of his > colleagues (who graduated from some from the most prestigous technical > colleges on this planet) were pissed off at his remuneration package - > they had 5-8 years exp and he just 1. So much for being gifted. > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > That's all crap. > Find a counterexample. Happy hunting. > Here are a few interesting figures that someone will probably bring > up: > - Richard Feynman's IQ was 125. James Gleick's biography, page 30: > Still, his score on the school IQ test was a merely respectable 125. > I'd wager this result was some sort of ßuke, but regardless of his > IQ per se, it's clear that from a young age Feynman had a considerable > amount of talent in math and science. Unfortunately that cannot be > said of an IQ-120-something person such as myself. > - The average IQ of a Nobel Prize winner (not sure whether this is in > any field or in the physical sciences) is somewhere in the 120 > range. I heard this from the Test The Nation televised IQ test > (which I did and got a 123 on, although the actual score would be a > bit higher given it started at age 18). Anyway, I've done some > research and never found where this statistic actually comes from. > Can anyone enlighten me? > Crap. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > > I value education. In fact, being non-gifted gives me even more of a > reason to value education... so I can work toward reaching my true > potential (albeit a somewhat limited potential). Why should I work my > ass off studying something that comes easy to others, when I could > just go into something less... intellectual demanding. > > Speaking of certain intellectual demands, would I be better off > choosing a different scientific field? Maybe my IQ would prevent me > from being a mathematician, but how about something like, say, > psychology? Maybe that's a bad example... would anyone care to offer > a list of low-IQ fields? > > Why should I be interested in math and science in the first place? It > seems that most people with average IQs (say, within 1 s.d. from the > mean) have little or no qualms about being average. They're more > concerned with earthly things, such as their appareance, crappy music, > television, etc. I like to think that I've elevated myself from this. > Not that I'm any better than these people, just that I'm not a > materialist. I've made the pursuit of knowledge the most important > pursuit in my life, because knowledge combats ignorance. Knowledge is > our criteria for evaluating new knowledge, for making decisions and > setting priorities. I've chosen to study math and science namely > because I'm fascinated by these subjects. But additionally, I often > think to myself that I won't have a better opportunity than now to > gain an understanding of these subjects. My dad is in his forties and > can't have more than a middle school understanding of math. There's > nothing stopping me from switching to some liberal arts major, placing > out of calculus, and taking the minimum number of science electives > via xxxx for non-majors courses. But what would I think of that > decision when *I'm* 40? I could pick up a graduate level psychology > paper right now and comprehend a pretty good deal of it. But give me > or just about any other (sane) human being a paper on the topology of > k-manifolds [insert more geordi-from-star-trek-talk here] and there's > no way in Hell I'll comprehend a bit of it. > > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > > Wow I've spent a lot of time writing this post. Anyway, I'd be really > interested in your replies. I'm particularly interested in knowing if > there is anyone reading this who is/was in a similar situation as I > am. And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > > I better be getting to bed... > Your obsession with IQ's is a reßection of your unfounded faith in > the system. > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Once you understand > that, then all your concerns will be addressed. > Those fields are totally off topic for this discussion. Are you under the > impression that advances in math come from Walmart? > Slainte, > Fletch === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > > Do programming. I know a guy who graduated just over a year ago from > comp. sci. and makes 45% more than the Physics Professors at the > institution he attended (fairly respectable for his field of study) > and 25% more than his comp. sci professors. > If you have a 120 IQ and you get into a TOP comp sci school, you are > probably a dead d unless you don't need sleep. > The school I'm planning on attending is in the top 10. Unfortunately > (or maybe fortunately), I didn't get into their special honors CS > program (I could transfer into it, though). Which brings me to a > slightly unrelated question... how important is it to be in honors > classes and programs, for grad schools and jobs and such? If the > school already has a good reputation and I get an outstanding GPA > without honors of any sort, is that enough? I'd suppose it's at > least better than doing poorly in such classes. What school are you attending? What department? > As for the sleep comment... unfortunately I need a pretty good deal of > it to function adequately, which puts me at an additional > disadvantage. The very best of the best are both brilliant and don't > sleep much... the last two valedictorians at my high school averaged 4 > hours of sleep a night. NoDoz and Ritalin, yummy. > One strategy I'm seriously planning on implementing is this: I'm going > to try to study wayy ahead of the curriculum in math and CS and > hopefully gain a pretty solid knowledge of the courses I'll be taking > *before* I ever actually take them. Maybe it's overkill, though. As many have said, do what you can and what you enjoy. You sound like a pretty motivated person. Find what you love and be happy. Slainte, Fletch === Subject: Re: Are there any non-gifted scientists?!?!? Fletch F. Fletch < > As many have said, do what you can and what you enjoy. You sound like a > pretty motivated person. Find what you love and be happy. > Slainte, > Fletch Yep. Dont become a slave to work or materialism. Work to live, dont live to work. Unless you really get ly and find a persuit that marries the two happily. Rob === Subject: Re: Are there any non-gifted scientists?!?!? > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. Dunno that word: it sounds a bit French. Is it derived from the French beau meaning beautiful. Does it mean rule by beauty or by beautiful people? === Subject: Re: Are there any non-gifted scientists?!?!? > ALMOST ALL academic fields (medical, some science, political, > religious, political) are USELESS BEAUROCRACIES. >Dunno that word: it sounds a bit French. Is it derived from >the French beau meaning beautiful. Does it mean rule by >beauty or by beautiful people? I think it's latin for not giving funding to morons who post their drivel on sci.math. -- I'm not interested in mathematics that might have anything to do with reality. -- Russell Easterly, in sci.math === Subject: Re: Are there any non-gifted scientists?!?!? Der Fugue skrev i meddelandet >I'm a high school student, about to go to college to study math and/or >computer science. I'm basically a nerd, been interested in >programming for a while but looking back I had a pretty distorted view >of what programming actually was when I was hacking away at code in >elementary school and middle school (I'm sure plenty of you had >similar experiences). More recently I've picked up math as a hobby >and become more of a science nerd than a computer nerd. >Here's my dilemma: I ain't that smart. Failed my school's gifted test >each time I took it, usually score in the 120s on online IQ tests >(except a 150 on the obviously rigged iqtest.com test). That alone >wouldn't be a tragedy, except for the fact that my high school grades >are pretty average... at least for an honors kid. This year, >schoolwork has become my *obsession*, and while my grades improved >from B's and C's to A's and B's, these weren't quite the grades I was >looking for, especially considering my courseload is rather light. Well what does an IQ test measure? To see patterns as fast as possible i believe. Thats good if you need structure in a process already found. But if you want to be an inventer you need creativity. A combination is good of course. What if reality has no order? Then todays math is useless for finding the truth. But if you just want to develop a new type of vacuum cleaner then its great. === Subject: Re: Are there any non-gifted scientists?!?!? (snip) And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > I better be getting to bed... Can't get no sleep... Anyway, as for naming respected physicists, I read somewhere (some reference book at the library) that Einstein's elementary school teacher was quoted as saying: He wouldn't amount to anything special.... To which Einstein was reportedly to have responded (but not confirmed): How many Nobel prizes has he won...? But that aside, having watched a number of interesting OU learning zone programs, the top brass consider software engineering as more of an Art rather than a science of which Maths is extremely important. As for the Test the Nation IQ test, I would rely on your score from that, I've read in a number of places (including the following weeks Radio Times) that the whole thing was watered down so that those who were not very good did average and people with normal - above higher than normal IQ's seemed like geniuses... === Subject: Re: Are there any non-gifted scientists?!?!? X-no-archive: yes > Anyway, as for naming respected physicists, I read somewhere (some > reference book at the library) that Einstein's elementary school > teacher was quoted as saying: > He wouldn't amount to anything special.... > To which Einstein was reportedly to have responded (but not > confirmed): > How many Nobel prizes has he won...? einstein was an adult in 1901 when the nobel prize was first awarded so i doubt its true :) sammi === Subject: Re: Are there any non-gifted scientists?!?!? X-no-archive: yes > einstein was an adult in 1901 when the nobel prize was first awarded > so i doubt its true :) rubbish rubbish rubbish, i misread the quote :) sammi === Subject: Re: Are there any non-gifted scientists?!?!? > I'm a high school student, about to go to college to study math and/or > computer science. I'm basically a nerd, been interested in > programming for a while but looking back I had a pretty distorted view > of what programming actually was when I was hacking away at code in > elementary school and middle school (I'm sure plenty of you had > similar experiences). More recently I've picked up math as a hobby > and become more of a science nerd than a computer nerd. > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. This year, > schoolwork has become my *obsession*, and while my grades improved > from B's and C's to A's and B's, these weren't quite the grades I was > looking for, especially considering my courseload is rather light. You should just forget IQ. Your ability to recognise shapes and patterns is only very loosely correlated to your abilities at any career whatsoever. It just makes me so angry when personnel departments insist of some kind of aptitude test. IQ is a complete load of rubbish, and you can train at them in the same way that you can learn how to become a good chess player, or crossword solver. Your education is something you only get once, but my main advice is to read a lot. Yes, you should study hard at school, it's money in the bank, the earlier you develop, the further you can get. But even if you hate many subjects at school does not make you dumb. You can be a late starter, take Einstein. Mensa is for people smarter-than-average, but not smart enough to realise it's a money-gathering exercise. === Subject: Re: Are there any non-gifted scientists?!?!? > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. Some old stats I remember put academics at an 120-140 IQ range - if you go too high, academic success actually gets more difficult. So you'd be fine. Then an IQ is not a single assessment of your abilities - most IQ tests determine your aptitude in several fields, and some are more important to your field of study than others. IQ scores do not remain constant over time, some published opinions notwithstanding. They depend on the test, and on the way you exercise your brain. (School kid's scores drop a few points over the summer vacation). Your high school grades are to be taken with a grain of salt as well - grades are usually quite subjective, depending a lot on the teachers. from studying the field that interests me! You're certainly not in a position that rules out success in the field. Learning to work hard and self-deisciplined is a big plus in academia. If you have now learned how to do this, you have a head start on a lot of the more gifted students who never had to (and suddenly find they need to). Oh, and don't be discouraged by maths: as you should have found out by now, there's a structure of building things on top of other things, so it's hard if you look at some top-level stuff and don't have the foundations yet. Michael -- Feel the stare of my burning hamster and stop smoking! === Subject: Re: Are there any non-gifted scientists?!?!? > Here's my dilemma: I ain't that smart. Failed my school's gifted test > each time I took it, usually score in the 120s on online IQ tests > (except a 150 on the obviously rigged iqtest.com test). That alone > wouldn't be a tragedy, except for the fact that my high school grades > are pretty average... at least for an honors kid. > Some old stats I remember put academics at an 120-140 IQ range - if you > go too high, academic success actually gets more difficult. So you'd be > fine. If I were you, I wouldn't put research mathematicians in the same category as those thousands and thousands who endlessly deconstruct literature, and then take an IQ sampling. Math gets very, very hard, perhaps without limit. I'm guessing that an IQ 120 person would reach frustration well before reaching the current fringes of math where research is done. I like Penny's idea of a high school math teacher. Can you imagine a good math teacher in every high school? Wonderful. I know a school that could use one. Slainte, Fletch > Then an IQ is not a single assessment of your abilities - most IQ tests > determine your aptitude in several fields, and some are more important > to your field of study than others. > IQ scores do not remain constant over time, some published opinions > notwithstanding. They depend on the test, and on the way you exercise > your brain. (School kid's scores drop a few points over the summer > vacation). > Your high school grades are to be taken with a grain of salt as well - > grades are usually quite subjective, depending a lot on the teachers. > from studying the field that interests me! You're certainly not in a > position that rules out success in the field. > Learning to work hard and self-deisciplined is a big plus in academia. > If you have now learned how to do this, you have a head start on a lot > of the more gifted students who never had to (and suddenly find they > need to). > Oh, and don't be discouraged by maths: as you should have found out by > now, there's a structure of building things on top of other things, so > it's hard if you look at some top-level stuff and don't have the > foundations yet. > Michael > -- > Feel the stare of my burning hamster and stop smoking! === Subject: Re: Are there any non-gifted scientists?!?!? Science is 10% inspiration and 90% perspiration (like so many other things in life). There is certainly room for scientists who are not geniuses, but who have perseverence to perform experiments and measurements carefully and repeatedly or to work hard on mathematical theories to figure out their consequences. In fact, being a genius will not in itself make you a scientist -- you need to be able to work hard and be critical of your own work and results. Torben === Subject: Re: Are there any non-gifted scientists?!?!? >Science is 10% inspiration and 90% perspiration (like so many other >things in life). There is certainly room for scientists who are not >geniuses, but who have perseverence to perform experiments and >measurements carefully and repeatedly or to work hard on mathematical >theories to figure out their consequences. In fact, being a genius >will not in itself make you a scientist -- you need to be able to work >hard and be critical of your own work and results. > Torben I agree fully. Consider chemistry especially if you are good at experimental work. I've spent a lifetime doing chemistry and am still doing it as a university gratis worker. In addition I've taken up trying to apply statistical reasoning to the game of bridge. It requirers no advanced math. Stig Holmquist === Subject: Re: Are there any non-gifted scientists?!?!? > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. It may be a sufficient condition (although I doubt it), but it's by no means a necessary one. Plenty of people with high IQs find math difficult--I married one of them. Her tested IQ during school was 185. Most of her high-IQ friends found math difficult. Most of MY high-IQ friends found math difficult. In fact, I've never actually known anyone for whom math came easy, regardless of their IQ! > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. I've found that people don't tend to quote their IQ scores unless those scores are above average. For instance, I've yet to see anyone jump into a conversation about IQs to offer their tested score of 80. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. And l. > But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? Work more. Expect to sacrifice things in your life you'd rather not sacrifice. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. This statement should trouble you far more than your IQ. If you're not only not having fun with math, but feel like studying it is a waste of your life, then for the love of God study something else! Even if you had math talent out the butt, if math is a drag for you, you're not going anywhere in the field. > And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. If they're respected in their field, are they not gifted? Point is, there's a lot of giftedness out there that isn't measured by IQ tests. === Subject: Re: Are there any non-gifted scientists?!?!? > intellectual ability. Talent in math and the sciences exists, it > certainly isn't completely accounted for by IQ but I'm sure IQ plays a > large role in it. > It may be a sufficient condition (although I doubt it), but it's by no > means a necessary one. Plenty of people with high IQs find math > difficult--I married one of them. Her tested IQ during school was 185. > Most of her high-IQ friends found math difficult. Most of MY high-IQ > friends found math difficult. In fact, I've never actually known anyone > for whom math came easy, regardless of their IQ! > I've met a lot of people with similar intellectual interests as I do > and read many a usenet IQ debate among such people, and I've yet to > encounter a person successful in mathematics or a hard science who > does not have a great deal of talent in the subject. This usually > means IQ > 130. > I've found that people don't tend to quote their IQ scores unless those > scores are above average. For instance, I've yet to see anyone jump into > a conversation about IQs to offer their tested score of 80. > As has often been said to me and as I'm sure many of you folks will > advise, it's all about hard work. > And l. > But even if I could force myself to > work twice as hard as everyone else and get the grades and coursework > necessary to go to grad school, what do I do next when the work > becomes even more challenging? > Work more. Expect to sacrifice things in your life you'd rather not > sacrifice. > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. > This statement should trouble you far more than your IQ. If you're not > only not having fun with math, but feel like studying it is a waste of > your life, then for the love of God study something else! Even if you > had math talent out the butt, if math is a drag for you, you're not going > anywhere in the field. Math can be extremely fun when I tackle a hard problem or learn a difficult concept. But at least for me, there's a lot of brutal work necessary leading up to that. You cannot tell me that the classical pianist *loves* playing scales, but he still does it, does he not? My problem is that I often find myself playing scales so-to-speak all day and fail to make considerable progress. Math is a lot more fun if it comes easily to you, namely because you're spending a greater proportion of your time doing fun and interesting things than you are doing endless exercises and reading, re-reading, and re-reading yet again to make sense of something. > And referring back to the subject text, I'm wondering if anyone > can name some names. Name me a few respected mathematicians, computer > scientists, physicists, any field will work actually, who are not > gifted. > If they're respected in their field, are they not gifted? Point is, > there's a lot of giftedness out there that isn't measured by IQ tests. === Subject: Re: Are there any non-gifted scientists?!?!? > .... > Math can be extremely fun when I tackle a hard problem or learn a > difficult concept. But at least for me, there's a lot of brutal work > necessary leading up to that. You cannot tell me that the classical > pianist *loves* playing scales, but he still does it, does he not? > My problem is that I often find myself playing scales so-to-speak all > day and fail to make considerable progress. Math is a lot more fun if > it comes easily to you, namely because you're spending a greater > proportion of your time doing fun and interesting things than you are > doing endless exercises and reading, re-reading, and re-reading yet > again to make sense of something.... Yes, practise your scales, but also play some light-hearted things to enjoy (Schubert dances?). Perhaps right now you would enjoy reading one or two of the very fine overview books which give real insight into mathematics. My usual first suggestion is Richard Courant and Herbert Robbins, What is Mathematics?, or one of the little books by W.W. Sawyer. Your response to those will tell you something about yourself in the mathematical world. Your original message maintained an earnest conscience, but your real love of mathematics and science kept glinting through the chinks. Don't stiße it! Your articulateness suggests that you may like to learn more about the arts as well, so by all means do that if you have the time and interest. Part of the pleasure of mathematics is in seeing its relationship with many other areas of human culture (in the broad sense of culture, which includes engineering for example). Don't overlook mathematical statistics. Many people (including physicists) have a very shallow idea of what it is. After you know enough basic calculus, a good introduction to statistical theory could be a real eye-opener in many ways. I shan't add any more to the multitude of good and bad replies, partly because they already include the particularly wise comments of gswork. Ken Pledger. === Subject: Re: Are there any non-gifted scientists?!?!? > .... > Math can be extremely fun when I tackle a hard problem or learn a > difficult concept. But at least for me, there's a lot of brutal work > necessary leading up to that. You cannot tell me that the classical > pianist *loves* playing scales, but he still does it, does he not? > My problem is that I often find myself playing scales so-to-speak all > day and fail to make considerable progress. Math is a lot more fun if > it comes easily to you, namely because you're spending a greater > proportion of your time doing fun and interesting things than you are > doing endless exercises and reading, re-reading, and re-reading yet > again to make sense of something.... > Yes, practise your scales, but also play some light-hearted things >to enjoy (Schubert dances?). Perhaps right now you would enjoy reading >one or two of the very fine overview books which give real insight into >mathematics. My usual first suggestion is Richard Courant and Herbert >Robbins, What is Mathematics?, or one of the little books by W.W. >Sawyer. Your response to those will tell you something about yourself >in the mathematical world. ... > Don't overlook mathematical statistics. Many people (including Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability by Colin Bruce. Sherlock Holmes explains probability and other mathematical concepts to Dr. Watson as he employs them in his work. Thoroughly enjoyable. -- Suppose you were an idiot... And suppose you were a member of Congress... But I repeat myself. - Mark Twain === Subject: Re: Are there any non-gifted scientists?!?!? > At the same time, I wonder if I'm going to be wasting arguably the > best years of my life studying the stuff. I guess the big issue for > me is *how much* commitment I want to put into it. Obviously I need > to keep my life balanced with other interests and reserve some time > for fun no matter what I decide to do. If its just for money in the bank and food on the table there are better offers. Futures trading! === Subject: Re: Are there any non-gifted scientists?!?!? 1) IQ ain't everything. 2) Albert Einstein ßunked algebra. 3) The art of study IS the art of science. 4) Do you like it? -- I'm a war president. I make decisions here in the Oval Office in foreign policy matters with war on my mind. - Bush === Subject: Re: Are there any non-gifted scientists?!?!? >2) Albert Einstein ßunked algebra. Nope. He did fail his first attempt at the entrance exam for E.T.H. Zurich, but that was because of French, chemistry and biology, which he hadn't bothered to study. See e.g. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: Are there any non-gifted scientists?!?!? >1) IQ ain't everything. >2) Albert Einstein ßunked algebra. >3) The art of study IS the art of science. >4) Do you like it? >-- >I'm a war president. I make decisions here in the Oval Office > in foreign policy matters with war on my mind. - Bush There's your answer! Nobody likes politicians with huge IQs (the smart ones usually play down their intelligence). Seriously, you'd want to be a bit of a maths whiz to prosper in physics or math, but I doubt the same would apply to (say) biology. Or most types of engineering, including software engineering*. Probably the biggest obstacle, indeed, is the over-academisation of university courses. Getting a degree - any degree - will require learning to spout a lot of theory that will never be used afterwards by most. *There is no such thing as computer science! - Gerry Quinn === Subject: Re: Are there any non-gifted scientists?!?!? >1) IQ ain't everything. >2) Albert Einstein ßunked algebra. >3) The art of study IS the art of science. >4) Do you like it? >-- >I'm a war president. I make decisions here in the Oval Office > in foreign policy matters with war on my mind. - Bush > There's your answer! Nobody likes politicians with huge IQs (the > smart ones usually play down their intelligence). with the highest IQ was dropped from the space program. Johnson's reply: Nobody likes a smart astronaut. === Subject: Re: Are there any non-gifted scientists?!?!? > or math, but I doubt the same would apply to (say) biology. Or most > types of engineering, including software engineering*. Probably the > *There is no such thing as computer science! Contrary to what engineers believe, computer science is NOT about writing market software. J === Subject: Re: Are there any non-gifted scientists?!?!? > *There is no such thing as computer science! Tell that to Alan Turing, or Donald Knuth, or... People who say this do not know what science means. Not many people do the science part of computing. Many colleges that say they teach computer science actually only teach a little if any of it. They teach how to make programs and computer science really doesn't fit into it. Have a look at the citeseer database. -- I'm a war president. I make decisions here in the Oval Office in foreign policy matters with war on my mind. - Bush === Subject: Re: Are there any non-gifted scientists?!?!? > *There is no such thing as computer science! >Tell that to Alan Turing, or Donald Knuth, or... >People who say this do not know what science means. Not many people >do the science part of computing. Many colleges that say they teach >computer science actually only teach a little if any of it. They teach >how to make programs and computer science really doesn't fit into it. The creation and study of computers is part of technology. The creation of software is part of engineering. Algorithmic information theory is part of maths. (The study of software I would place in technology or maths.) Science is the study of the natural world (appropriate subject-object distinctions may allow fields like anthropology to be included). No significant field of science so far exists relating to computers. - Gerry Quinn === Subject: Re: Are there any non-gifted scientists?!?!? > *There is no such thing as computer science! > Tell that to Alan Turing, or Donald Knuth, or... > People who say this do not know what science means. Not many people > do the science part of computing. Many colleges that say they teach > computer science actually only teach a little if any of it. They teach > how to make programs and computer science really doesn't fit into it. When Thinking Machines started they were faced with a dilemma. The cost of a custom CPU was a sensitive function of the number of its on-chip communications buffers (die area). The difference between profit and penury was one buffer. Computer science was more than capable of calculating how many buffers were needed: One more than they could afford. These were Feynman accolytes. Feynman did the calculation using differential equations that tacitly assumed continuous functions, not digital data. Feynamn said they could get by with one fewer buffer. No sweat. You are a bunch of greenhorns with no reputation. Your miraculous startup has a few $million in investor cash. Once you spec your CPU there is no going back. If you screw up there is 100% disaster and probably jail time. The only way to know the real world answer is to do it - and you cannot make just one. All or nothing. Do you trust the validated work of hundreds of acknowledged specialists in the field, your field, or do you go with ßakey Feynman diddling where he doesn't belong because he is bored? Could everybody *except* Feynman be wrong? Danny Hillis' decision bet the rest of everybody's lives and $millions that weren't his on the outcome. The MBA route was to manufacture the sure-thing chip they couldn't afford and amortize short-term losses against future revenues. Thinking Machines bet its Connection Machine on Feynman's unsubstantiated analysis. It was an irresponsible and insane thing to do. Any decent venture capitalist would have immediately filed civil and criminal charges against the corporate officers to recover investor funds and punish the wicked. http://www.cs.nyu.edu/cs/faculty/shasha/outofmind/ hillisfeyn.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! === Subject: Re: Are there any non-gifted scientists?!?!? > Do you trust the validated work of hundreds of acknowledged > specialists in the field, your field, or do you go with ßakey Feynman > diddling where he doesn't belong because he is bored? Could everybody > *except* Feynman be wrong? Danny Hillis' decision bet the rest of > everybody's lives and $millions that weren't his on the outcome. How did Danny make out business-wise? As well as the less gifted Bill Gates? Talk all ye will of talent and genius, it is money that is taken to the bank. My father used tell me of geniuses that drove taxicabs during the Great Depression. Bob Kolker === Subject: Re: Are there any non-gifted scientists?!?!? >1) IQ ain't everything. >2) Albert Einstein ßunked algebra. >3) The art of study IS the art of science. >4) Do you like it? >-- >I'm a war president. I make decisions here in the Oval Office > in foreign policy matters with war on my mind. - Bush >There's your answer! Nobody likes politicians with huge IQs (the >smart ones usually play down their intelligence). >Seriously, you'd want to be a bit of a maths whiz to prosper in physics >or math, but I doubt the same would apply to (say) biology. You have got to be kidding. I take it you never took any classes after the birds and the bees class. > .. Or most >types of engineering, including software engineering*. You don't have clue. /BAH Subtract a hundred and four for e-mail. === Subject: Re: Are there any non-gifted scientists?!?!? >Seriously, you'd want to be a bit of a maths whiz to prosper in physics >or math, but I doubt the same would apply to (say) biology. >You have got to be kidding. I take it you never took any >classes after the birds and the bees class. I never took biology classes, but I'd imagine that a good grasp of mathematical tools like statistics would have you sorted for at least 95% of the field. For which you don't have to be a maths whiz. > .. Or most >types of engineering, including software engineering*. >You don't have clue. Show me a civil or mechanical engineer who needs to be brilliant at math. Maybe some electronic engineers and a very few chemical engineers need it. Others just need to be highly numerate, and be good at using mathematical tools. Software engineers may need a bit more, but nothing I'd class as needing to be a wizard at it. There's a lot of systematic crunching of complex algorithms, but not the sort of stuff a real mathematician would need to handle. - Gerry Quinn === Subject: Re: Are there any non-gifted scientists?!?!? X-no-archive: yes > I never took biology classes, but I'd imagine that a good grasp of > mathematical tools like statistics would have you sorted for at least > 95% of the field. For which you don't have to be a maths whiz. no, it's done with stats packages such as spss. sammi === Subject: Re: Are there any non-gifted scientists?!?!? > *There is no such thing as computer science! That depends on how you define computer science. -- Thomas. === Subject: Re: Are there any non-gifted scientists?!?!? >I'm a high school student, about to go to college to study math and/or >computer science. I'm basically a nerd, been interested in >programming for a while but looking back I had a pretty distorted view >of what programming actually was when I was hacking away at code in >elementary school and middle school (I'm sure plenty of you had >similar experiences). More recently I've picked up math as a hobby >and become more of a science nerd than a computer nerd. >Here's my dilemma: I ain't that smart. Failed my school's gifted test >each time I took it, usually score in the 120s on online IQ tests >(except a 150 on the obviously rigged iqtest.com test). That alone >wouldn't be a tragedy, except for the fact that my high school grades >are pretty average... at least for an honors kid. This year, >schoolwork has become my *obsession*, and while my grades improved >from B's and C's to A's and B's, these weren't quite the grades I was >looking for, especially considering my courseload is rather light. Studying hard right now is a good idea, because it gives you loads of options later on. If you aim to be a scientist and fail you will probably get a decent choice of jobs: in this sense it is far more sensible than aiming to be a professional athlete. Are you including statistics in with maths? In lots of fields, you can't do science without it, and learning it gives you a close look at what finding the truth boils down to. OTOH - the chances of ending up a successful scientist - even given an excellent school record - are IMHO about the same as the chances of ending up a professional athlete so deciding that only this will satisfy you is probably not a good idea. (By successful I mean producing new work that people outside a very limited circle would read and appreciate without having to be paid). If you are looking for a vocation, have you considered something health- related? In that area, everything from scrubbing ßoors up - if done well - really does save lives. In fact, in theory the existence of any paying job means that somebody thinks what you are doing is useful though I have some doubts about some jobs in large bureaucracies. -- A. G. McDowell === Subject: Re: Are there any non-gifted scientists?!?!? X-URL: http://mygate.mailgate.org/mynews/comp/comp.theory/ 3af86db11bde017d1b5d6d1d9 0 4aa847.48257%40mygate.mailgate.org > OTOH - the chances of ending up a successful > scientist - even given an excellent school record > - are IMHO about the same as the chances of ending > up a professional athlete so deciding that only > this will satisfy you is probably not a good idea. > (By successful I mean producing new work that > people outside a very limited circle would read > and appreciate without having to be paid). That's not successful, that's famous, like Carl Sagan. Successful is in contrast to the maintenance occupations, that you leave something of worth behind when you are gone, rather than merely fighting mess and entropy all your career, or building stuff that wears out and gets thrown away. In _that_ sense of successful, lots of folks with very modest intellectual skills are world-class successful, in the arts as well as the sciences. To the OP: A 120 IQ is in the top quarter, and not everyone has to be _lead_ scientist to be a successful scientist. There's plenty of room for the non-gifted. I never was the person in charge of a science research effort. Every science project in which I've ever participated had lots of folks like me, team members following the direction of team leaders with better education and more experience. We were people who could do what we were told, gathering data and running experiments and analyzing data into summary data, and not make a mess of it. We were still successful scientists who could feel like we were personally advancing the knowledge of the human race with our efforts every day. [In my case this included some pretty spectacularly memorable ways when at sea. Driving a ship into hurricane force winds in the dark of night and trying to stay in one fixed spot while the ocean did its best to batter us all to pudding isn't a thing you want to do more than once, but the once is a story you can repeat for years afterwards.] I got to support Oceanography, Meteorology, Gravimetry, Hydrography, Ecology Health Monitoring, Biology, Zoology, and Satellite Communications, over a long career, even though I graduated from college with a stunning C+ average, and I got to do some original Hydrographic survey new technique invention work that was published at least in-house. Good math skills let me become a successful computer programmer, and that was where I made many of my contributions to scientific research. If you keep up your math and computer skills, they will be welcome in almost any branch of science that interests you, from astronomy to zoology. And don't discount the willing to work hard part. It got me As as far as I could go in grad school without any splendid talents, and a really good opinion from my bosses, peers, and subordinates over the years. xanthian. -- === Subject: Re: Are there any non-gifted scientists?!?!? >Here's my dilemma: I ain't that smart. Failed my school's gifted test >each time I took it, usually score in the 120s on online IQ tests >(except a 150 on the obviously rigged iqtest.com test). That alone >wouldn't be a tragedy, except for the fact that my high school grades >are pretty average... at least for an honors kid. This year, >schoolwork has become my *obsession*, and while my grades improved >from B's and C's to A's and B's, these weren't quite the grades I was >looking for, especially considering my courseload is rather light. > Studying hard right now is a good idea, because it gives you loads of > options later on. If you aim to be a scientist and fail you will > probably get a decent choice of jobs: in this sense it is far more > sensible than aiming to be a professional athlete. Are you including > statistics in with maths? In lots of fields, you can't do science > without it, and learning it gives you a close look at what finding the > truth boils down to. > OTOH - the chances of ending up a successful scientist - even given an > excellent school record - are IMHO about the same as the chances of > ending up a professional athlete so deciding that only this will satisfy > you is probably not a good idea. (By successful I mean producing new > work that people outside a very limited circle would read and appreciate > without having to be paid). Without that particular measure, and noting that science which isn't read outside of the technical field often does lead to life enhancing technology that does [reach others] (e.g. in medical science), Ôsuccessful scientists' would number a great many more. > If you are looking for a vocation, have you considered something health- > related? In that area, everything from scrubbing ßoors up - if done > well - really does save lives. In fact, in theory the existence of any > paying job means that somebody thinks what you are doing is useful > though I have some doubts about some jobs in large bureaucracies. I tend to agree, in fact it's the basic argument for free trade - that other people find use value in what you produce and can make their demand for that product Ôeffective' by trading something useful themselves - so every one is engaged in evidently useful stuff! An idealised summary for sure, and given what some people find useful often less than what one might hope, but better, IMO, than a command economy in which every one is forced into producing something considered useful only to a small political power wielding elite! [*] * oddly, also the basis of many a critique of free trade! === Subject: Re: Cantor Challenge >I challenge anyone who thinks that the reals are countable to make me >a countable list of reals such that it is impossible to have a number >not on the list. I will use a method other than Cantor's diagonal >method to make one. > >William S. > I think the non-Cantorians could give you a really hard time here. > I will give an enumeration of all the real numbers 0<= x <= 1. No you won't! > Start with the factorial base since every rational number has > a finite representation in this base. This is a challenge:you provide the list, then I look for real number not in the llist. I can require that when you list is completed that it be represented in a base of my choosing, at lesat to the extent that the n'th number is carried out to at least n+2 places in an integer base greater than 3. Then the Cantor diagonal algorithm for that base will produce a number not in your list. Challenge met, Cantor vindicated! > x = a1/2! + a2/3! + a3/4! + ... > .0 = 0 > .1 = 1/2 > .01 = 1/6 > .11 = 1/6 + 1/2 = 2/3 > .02 = 2/6 = 1/3 > .12 = 2/6 + 1/2 = 5/6 > ... > Given any rational number, 0 <= q <= 1, > I can give an natural number, n, that is the > position of q in my list. > Now, lets get all those irrational numbers. > The generic version of the factorial base is the series: > 1/2, 1/6, 1/6, 1/24, 1/24, 1/24, ... > 1/e does not have a finite representation in base factorial. > Define a new series: > 1/e, 1/2-1/2e, 1/4-1/4e, ... > Combine this series with the factorial base series. > 1/2, 1/e, 1/6, 1/6, 1/2-1/2e, 1/24, 1/24, 1/24, 1/4-1/4e, ... > Using this new base: > .0 = 0 > .1 = 1/2 > .01 = 1/e > .11 = 1/e + 1/2 > .001 = 1/6 > .101 = 1/6 + 1/2 = 2/3 > .011 = 1/6 + 1/e > .111 = 1/6 + 1/e + 1/2 > .002 = 2/6 = 1/3 > ... > Assume that 1/PI does not have a finite representation in the above base. > Repeat the process to include numbers like 1/nPI: > Series that adds to 1 = 1/PI, 1/2-1/2PI, 1/4-1/4PI, ... > New base series = 1/2, 1/e, 1/PI, 1/6, 1/6, ... But you are now changing the list. At any stage, the list you have at that point is missing uncountably many reals. When you change the list to include some of the missing ones, others can be found still to be missing. No SINGLE list contains them all, because as soon as any list is completed, numbers not in it can be found. > I can do this for any countable number of irrational numbers. Countably many does not cut it. > The resulting generic bases are not very efficient. > For example, using the base 1/2, 1/e, 1/6, 1/6, ... > 1/2 has at least three different representations: > .1000... = 1/2 > .0020304... = 1/2 > .0100... = infinite 1/e representation of 1/2 > Since I am trying to list all the rational numbers between 0 and 1, > all that matters is that 1/2 has a finite representation. > I can now give a finite representation for every rational number > and any multiple of a countable number of irrational numbers. > Find a real 0 <= x <= 1 that is not in my list. Let the list be indexed by {1,2,3,...}, and let the n'th number be rounded off to the n'th decimal place. Construct the new number so that if the n'th digit of the rounded n'th number is 5 or more use a 1 in the new number's n'th place, otherwise use an 8. It does not matter how your list is constructed, this method constructs a number not in your list. Note that this does not require an exact representation of any listed number, only that each one can be approximated as closely as one wishes === Subject: Re: IBM BlueGene Super Computer > current record of 1,240,000,000,000 digits)? > Its not a matter of if it can be done, it could be done right now. It > would just take more memory and more disk space, and more time. To > compute the 1.24 trillion digits took 400 hours. If you are willing > to wait you could calculate and number of digits you want with current > technology. Now it would be true a faster machine could find the > digits quicker, but that was not your question. Ok, so it's possible. That answers my first question. Now, why hasn't anyone tried using these faster computers to set new records? === Subject: 1st before all Test message. Have I crowded in line before Ms.Hot me first @.@.? === Subject: Re: 1st before all > Test message. Have I crowded in line before > Ms.Hot me first @.@.? Test complete. Mr.Sir.Cool is 1st! Now for the next test ... or am I getting ahead of myself? ;-) === Subject: Four Color Theorem Here is the second step in a proof of the Four Color Theorem If R is a out[er]planar graph, then Chi(R)<=3. === Subject: Re: Four Color Theorem I don't think that FCT and HC can be proved in graph theory by human because something is lost in graph theory. Although they are represented in graph theory, I am sure that they are the space character, not the character of a graph. My idea is immature now, however, I should prove that it is impossible to prove FCT and HC in graph theory. Just going back to the start point, I obtained a proof of FCT and HC. Everyone else think that a map is equal to its dual graph, but it doesn't. When a map is replace by vertices and edges, the relation between R2 and R3 is also neglected. However, it is absolutely necessary to prove FCT and HC. The proof is here, http://arxiv.org/abs/math.GM/0311475 And to the expert in graph theory, the comments is here, http://caozx.100free.com/comment.pdf === Subject: Re: Dark Energy Hologram Entropy of Universe === >Subject: Re: Dark Energy Hologram Entropy of Universe >Message-id: > ok,..... But this should be posted in sci.drivel.bandwidthwaisters >[Hammond] >I notice that there are at least TWO serious scientists >who are both ignored and heckled on this newsgroup. >1. George Hammond >2. Jack Sarfatti >Hammond has apparently discovered the world's first >real scientific proof of God >and >Sarfatti is obviously the most competent mathematical-physicist >on the newsgroup. Does Sarfatti belive Hammond's proof of God? -- Mensanator Ace of Clubs === Subject: Re: PROOF that numbers are countable <5sknj1-afq.ln1@lexi2.athghost7038suus.net> <4069398d$0$16965$afc38c87@news.optusnet.com.au> <4069f669$0$20347$afc38c87@news.optusnet.com.au> <406e2ac8$0$12740$afc38c87@news.optusnet.com.au> <406e3e31$0$4574$afc38c87@news.optusnet.com.au> <406f9372$0$4545$afc38c87@news.optusnet.com.au> <1OFjc.1414$TT.15@news-server.bigpond.net.au> <408f9b15$1_4@newsfeed.slurp.net> <2SNjc.2628$TT.683@news-server.bigpond.net.au> > Perhaps because it was obvious to everyone except you that she was one > of the people it was directed at? > what exactly is the unachievable Barb is striving for? To make you see the light, although you have torn your eyes out long ago. Stephan === Subject: Re: PROOF that numbers are countable > > Perhaps because it was obvious to everyone except you that she was one > of the people it was directed at? > what exactly is the unachievable Barb is striving for? > To make you see the light, although you have torn your eyes > out long ago. ly for powerBraille. this mob you are so in awe of think taking the side of curriculum and published text is license to say anything. lets construct a function and get a contradiction on the diagonal is the tool of fools and you are their chaeffeur. pure lambda abstractions and turing machines themselves can construct *every function* and have them countable, without subfunctions. These systems are as powerful as all other computing systems, including your specific subfunction reliant paradox succeptible system that is the only system that your proofs produce their EVIDENTLY ABSTRACT conjectures. Define Function xyz (par1, par2) { *body* } is a construct by humans for humans, its not necessary. If you introduce it don't enforce its idiosyncracies on valid countable complete function sets. Herc === Subject: Re: PROOF that numbers are countable >Perhaps because it was obvious to everyone except you that she was one >of the people it was directed at? >what exactly is the unachievable Barb is striving for? >To make you see the light, although you have torn your eyes >out long ago. > ly for powerBraille. this mob you are so in awe of think taking the > side of curriculum and published text is license to say anything. > lets construct a function and get a contradiction on the diagonal is the > tool of fools and you are their chaeffeur. pure lambda abstractions > and turing machines themselves can construct *every function* and have > them countable, without subfunctions. These systems are as powerful > as all other computing systems, including your specific subfunction reliant > paradox succeptible system that is the only system that your proofs > produce their EVIDENTLY ABSTRACT conjectures. > Define Function xyz (par1, par2) { > *body* > is a construct by humans for humans, its not necessary. If you introduce > it don't enforce its idiosyncracies on valid countable complete function sets. It is not necessary, but it can be recoded into a register machine or turing machine program. It is therefore equivalent to a portion of a turing machine. -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: PROOF that numbers are countable > and turing machines themselves can construct *every function* and have > them countable, without subfunctions. These systems are as powerful > as all other computing systems, including your specific subfunction reliant > paradox succeptible system that is the only system that your proofs > produce their EVIDENTLY ABSTRACT conjectures. > Define Function xyz (par1, par2) { > *body* > } > is a construct by humans for humans, its not necessary. If you introduce > it don't enforce its idiosyncracies on valid countable complete function sets. > It is not necessary, but it can be recoded into a register machine or > turing machine program. It is therefore equivalent to a portion of a > turing machine. That would require F to be a subfunction emulated within UTM. G(j) = F(j,j) mod 2 + 1 has to compile to a godel number within the system used in UTM. Right? If UTM is simple, it will assign a godel number. Assume it allows function decomposition to determine the godel number of a function. If X compiles, then X mod 2 compiles If X compiles, then X + 1 compiles Therefore if F(x,y) was a subfunction, F(j,j) mod 2 + 1 would compile to a godel number, a godel number would be found that couldn't exist as a valid function in the system, its definition would differ to its value in F. Sounds self defeating, the assumption is that a UTM exists that has a clever godel scheme, not to find a particular impossible system. Herc === Subject: Re: PROOF that numbers are countable >I have to say I'm sincerely impressed with the patience of >a few people here in re-trying once and again to achieve >the unachievable... >what exactly is the *unachievable* they are striving for? >How is what you are doing different from what you accuse us of? Both >sides assume the praise is meant for them. Perhaps the author will >return and clarify the issue. > Because I can answer the above question while you have to skim over it. > Herc > The unachievable is getting you to see that Cantor's Diagonalization > argument is valid. That should be obvious to anyone who's still > following this thread. So in your interpretation, Steve is a long term follower of my Cantor theories and admires you for *re-trying* to debate me? Its not that the my theory seems wrong its the fact that I'm impervious to reason that he's pointing out, that my insistence on countable reals is impervious? This has been going on for such a long time its obvious, anyone kind enough to take it upon themselves to bring me from my false convictions, to RETRY and point out to me again and again? You point out the diag forms a new number somewhere in definition land, again and again and again you put forth Cantors proof, again and again an again it doesn't hold in my convictions? Its not negating Cantors proof that unachievable its getting people to understand it that's unachievable?? No you dip, read the whole paragraph and try to put it in context. I'm not the object of the long term study, Cantors proof OBVIOUSLY is. I know this is a different representation of what was written, but try to comprehend the intended MEANGING of what was written. Using juxtaposition of his sentences, just replace ... with , and see what it MEANS. It doesn't really matter how many sentences there are. a few people here in re-trying once and again to achieve the unachievable, Refutating Cantor's diagonalization proof better take that feather out of your cap. Herc === Subject: Re: PROOF that numbers are countable >I have to say I'm sincerely impressed with the patience of >a few people here in re-trying once and again to achieve >the unachievable... >what exactly is the *unachievable* they are striving for? >How is what you are doing different from what you accuse us of? Both >sides assume the praise is meant for them. Perhaps the author will >return and clarify the issue. >Because I can answer the above question while you have to skim over it. >Herc >The unachievable is getting you to see that Cantor's Diagonalization >argument is valid. That should be obvious to anyone who's still >following this thread. > So in your interpretation, Steve is a long term follower of my Cantor theories > and admires you for *re-trying* to debate me? No, I suspect he has seen a number of people saying Cantor was wrong because... and has respect for people who have the patience to explain the ßaws in their attacks on Cantor's diagonalization argument, most of which reduce to presenting a proof of something different and claiming it shows Cantor was wrong. He has probably also noticed that a number of the anti-Cantor people repeatedly fail to understand why they have not disproven the diagonalization argument. He apparently feels that patience in the face of unwillingness/inability to understand the ßaws in their disproofs is something admirable. > Its not that the my theory seems > wrong its the fact that I'm impervious to reason that he's pointing out, that > my insistence on countable reals is impervious? If your theory includes something to the effect that Cantor diagonalization with the axioms used is invalid, then your theory is wrong. It's the fact that you appear to be saying Cantor diagonalization doesn't work under my unstated axioms that has, IMO, dragged this particular discussion on for so long. > This has been going on > for such a long time its obvious, anyone kind enough to take it upon themselves > to bring me from my false convictions, to RETRY and point out to me > again and again? You point out the diag forms a new number somewhere in > definition land, again and again and again you put forth Cantors proof, again > and again an again it doesn't hold in my convictions? Its not negating Cantors > proof that unachievable its getting people to understand it that's unachievable?? It's getting us to the same set of axioms that seems to be unachievable. The fact that computability and enumerability are extremely precise topics that it is easy to get sloppy with doesn't help any. > No you dip, read the whole paragraph and try to put it in context. I'm not the > object of the long term study, Cantors proof OBVIOUSLY is. Cantor's proof, your axioms (whatever they are), and trying to state something that is mathematically correct that everyone can agree on when the terminology can get slippery has been the discussion. > I know this is a different representation of what was written, but try to comprehend > the intended MEANGING of what was written. Using juxtaposition of his sentences, > just replace ... with , and see what it MEANS. It doesn't really matter how many > sentences there are. > a few people here in re-trying once and again to achieve > the unachievable, Refutating Cantor's diagonalization proof > better take that feather out of your cap. > Herc Looking at his response, apparently the ... was to be replaced with . -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: PROOF that numbers are countable >I know this is a different representation of what was written, but try to >comprehend >the intended MEANGING of what was written. Using juxtaposition of his >sentences, >just replace ... with , and see what it MEANS. It doesn't really matter >how many >sentences there are. OK, let's play your word salad game, using this time a suitably re-presented >I don't actually read anything, just glance at the text and pattern match; >there is absolutely no way to get anything past, no matter how much >evidence -- don't comprehend or understand or reason or think AT ALL. And then you go on to say (quoted accurately): >Unbelievable, its going to take 5 years for me to program AI [...] and the >AI will have to explain to you what knee jerk simpletons you've all been >while I've been constantly telling you to listen. Before putting your unique talents to work solving the entire AI problem, you might want to have a look McDermott's classic essay, Artificial Intelligence Meets Natural Stupidity, available online at -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | ----------------------------- === Subject: Re: PROOF that numbers are countable >It doesn't really matter >how many >sentences there are. > OK, let's play your word salad game, using this time a suitably re-presented >I don't actually read anything, just glance at the text and pattern match; >there is absolutely no way to get anything past, no matter how much >evidence -- don't comprehend or understand or reason or think AT ALL. > And then you go on to say (quoted accurately): >Unbelievable, its going to take 5 years for me to program AI [...] and the >AI will have to explain to you what knee jerk simpletons you've all been >while I've been constantly telling you to listen. > Before putting your unique talents to work solving the entire AI problem, you > might want to have a look McDermott's classic essay, Artificial Intelligence > Meets Natural Stupidity, available online at I solved the AI problem a decade ago. Results 1 - 10 of about 21 for inverse computation author:|-|erc. (0.42 seconds Now should I make a simple enquiry how these sentence games are related to this knock-on : >I have to say I'm sincerely impressed with the patience of >a few people here in re-trying once and again to achieve >the unachievable... It's not quite that saintly . Yes, patience is necessary, but there also needs to be some motivation to bother with the net.cranks in the first and expect another tangential remark, you know Rugby Barb? Or confront you with more mathematical matters and see you posting related diatribe in another thread next week? Herc === Subject: A question about continuous bijections from R2 to R2 The problem is simple. Given a continuous bijection f from an open set U to an open set V of the normed vector space R^n, is f-1 also continuous ? Actually it is quite easy to find a counter-example when the sets U and V are not supposed to be open ... but this is not the problem stated. So what happens when U and V are open sets ? A.B. === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > So what happens when U and V are open sets ? All I can do is to tell you the same thing I told you when you've asked the same question at the fr.sci.maths newsgroup. There is no such counter example; see: http://en.wikipedia.org/wiki/Invariance_of_domain Jose Carlos Santos === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain I don't know much about invariance of domain, but doesn't this simple proof work? Any point in U has a compact neighborhood* contained therein. A continuous bijection from a compact space to a Hausdorff space is a homeomorphism. *For me (and others, e.g., Kelley), N is by definition a neghborhood of x iff x is in the interior of N. -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain > I don't know much about invariance of domain, but doesn't this simple > proof work? Any point in U has a compact neighborhood* contained > therein. A continuous bijection from a compact space to a Hausdorff > space is a homeomorphism. > *For me (and others, e.g., Kelley), N is by definition a neghborhood > of x iff x is in the interior of N. Congratulations, you've shown f is homeomorphic on compact subspaces of U. Now explain why this leads to the conclusion (true, but not so easy to prove) that f is homeomorphic on U. Let's take an explicit example where N is a closed ball containing x in the interior and maps under f to some compact thing f(N). As you have observed, f is a homeomorphism when restricted to N. To conclude that f is a homeomorphism on the entire domain U, you need to show that f maps interior of N to an open set. Certainly interior of N is open in N (where N has the subspace topology), so f(interior of N) must be open *in f(interior of N)*. You want to show it is *also* open in V. How do you do this? It's not a one-liner, that's for sure! Consider the example where f is a continuous bijection of the union of [0, 0.5] and (1.5,2] to [0, 1] given by just gluing the intervals together. This is not a homeomorphism, since f^-1 takes a connected set to a disconnected one. Take a neighborhood of 0.5, a compact interval with 0.5 as the right endpoint. This is open in the domain, e.g. 0.5 is an interior point. Certainly this neighborhood maps homeomorphically to a compact interval. But now the image of 0.5 is not an interior point. You've created boundary by mapping the neighborhood. This can happen in general, even for nice spaces like in our example, e.g. metrizable spaces. The fact that R^n does not have this kind of behavior is something very special about R^n. === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain > I don't know much about invariance of domain, but doesn't this simple > proof work? Any point in U has a compact neighborhood* contained > therein. A continuous bijection from a compact space to a Hausdorff > space is a homeomorphism. > *For me (and others, e.g., Kelley), N is by definition a neghborhood > of x iff x is in the interior of N. Hmm, I see the problem here: Let p be a point in U, K a compact neighborhood of p contained in U, and L = f(K). Then the restriction of f to K is a homeomorphism. Thus, given a neighborhood W of p, f(W) is a neighborhood of f(p) in L; however, I have not shown that f(p) is in the interior of f(W) in the topology of V. Is there an elementary way to show that f must map p to an interior point of L under the topology of V? I am thinking that there should be, since we are working in Euclidean space. I don't claim it to be so, though. -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain I must be missing something then. What if U is the points of R^2 more than 1 unit from the origin, and V is the points of R^2 other than the origin, and f(r, theta) = (r - 1, theta)? Looks to me like U is open, and V is open, and f is continuous, but f-inverse takes the points (epsilon, 0) and (epsilon, pi) to points separated by more than 2. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: A question about continuous bijections from R2 to R2 > > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > > http://en.wikipedia.org/wiki/Invariance_of_domain > I must be missing something then. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: A question about continuous bijections from R2 to R2 > > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > > http://en.wikipedia.org/wiki/Invariance_of_domain > I must be missing something then. > What if U is the points of R^2 more than 1 unit from the origin, > and V is the points of R^2 other than the origin, > and f(r, theta) = (r - 1, theta)? > Looks to me like U is open, and V is open, and f is continuous, > but f-inverse takes the points (epsilon, 0) and (epsilon, pi) > to points separated by more than 2. This is all true, but f-inverse is still continuous. I think the problem you are having is that you are looking at what happens in a neighborhood of the origin, when strictly speaking, it's not in the domain. What you need to do is look at a neighborhood of say, (epsilon, 0). === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain >I must be missing something then. >What if U is the points of R^2 more than 1 unit from the origin, >and V is the points of R^2 other than the origin, >and f(r, theta) = (r - 1, theta)? Then the inverse is the map g: V -> U defined by g(r, theta) = (r+1, theta), which is continuous on V. >Looks to me like U is open, and V is open, and f is continuous, >but f-inverse takes the points (epsilon, 0) and (epsilon, pi) >to points separated by more than 2. True. This does not show that g is not continuous. It shows that g is not _uniformly_ continuous. ************************ David C. Ullrich === Subject: Re: A question about continuous bijections from R2 to R2 > The problem is simple. Given a continuous bijection f from an open set > U to an open set V of the normed vector space R^n, is f-1 also > continuous ? Actually it is quite easy to find a counter-example when > the sets U and V are not supposed to be open ... but this is not the > problem stated. > > So what happens when U and V are open sets ? > All I can do is to tell you the same thing I told you when you've > asked the same question at the fr.sci.maths newsgroup. There is no > such counter example; see: > http://en.wikipedia.org/wiki/Invariance_of_domain > I must be missing something then. > What if U is the points of R^2 more than 1 unit from the origin, > and V is the points of R^2 other than the origin, > and f(r, theta) = (r - 1, theta)? > Looks to me like U is open, and V is open, and f is continuous, > but f-inverse takes the points (epsilon, 0) and (epsilon, pi) > to points separated by more than 2. This does change the fact that the inverse of f is continuous at every point of its domain. Or do you see any point of V at which the inverse of f is not continuous? Jose Carlos Santos === Subject: Re: Please help me!!! > I am unable to really get started with proving this question and I was > wondering if someone could please help me. Your help would greatly be > appreciated. > Question: Prove that if G is an abelian group and |G|=p1...pn where > the pi's are distinct primes, then G is a cyclic group. Prove it by induction, using the following lemma: Suppose we have a short exact sequence of abelian groups: 0 -> C -> G -> C' -> 0 where C and C' are cyclic groups of orders a and b respectively, and a and b are relatively prime. Then G is cyclic of order ab. [Note: I'm going to use multiplicative notation for the group operation in following proof.] Proof: Suppose C' is generated by c' and C is generated by c. Let g in G be an element mapping to c'. Then g^b belongs to C. Say g^b = c^d. Now, since a and b are relatively prime, we can find r and s such that ar + bs = 1. Put h = g c^(-sd). Then h^b = g^b c^(-bsd) = c^(d - bsd) = c^(d - d + ard) = identity. So, we've found an element h in G with order b, and so since c has order a, and a and b are relatively prime, ch must have order ab. Therefore, ch is a cyclic generator for G. === Subject: Re: Please help me!!! Here is a hint: If x and y are elements of a (finite) group, then | xy | = LCM ( | x |, | y | ) Also, a finite abelian group contains elements of order p, for every prime p dividing the order of the group. Hope this helps, Brian >I am unable to really get started with proving this question and I was >wondering if someone could please help me. Your help would greatly be >appreciated. >Question: Prove that if G is an abelian group and |G|=p1...pn where >the pi's are distinct primes, then G is a cyclic group. === Subject: velocities of the two ends of a sliding ladder Its related to the famous sliding ladder problem wherein a ladder rests against a wall making some angle with the ground initially and then suddenly starts sliding or the base can be moved at a constant velocity.The problem is to know the velocity of the vertical end or the CM of the ladder at any instant.? Now my confusion is.... How come the speeds of the two ends of the ladder are different as the vertical end travels the same distance in same time as the base (or bottom end) travels.?? So technically speaking the speeds of the two ends must be the same?? Then if we move the base with constant velocity why can't we assign the same speed to the vertically sliding end?? Yogesh === Subject: Re: velocities of the two ends of a sliding ladder > How come the speeds of the two ends of the ladder are different as the > vertical end travels the same distance in same time as the base (or > bottom end) travels.?? Speeds and distances covered are different,for the same time interval. Let x and y be intercepts on the coordinate axes. Since x^2+y^2=l^2,where l is ladder length,differentiate with time to get dx/dy = x-velocity/y-velocity = -y/x which is -1 only when ladder is at 45 degrees to ground. === Subject: Re: velocities of the two ends of a sliding ladder > Its related to the famous sliding ladder problem wherein a ladder > rests against a wall making some angle with the ground initially and > then suddenly starts sliding or the base can be moved at a constant > velocity.The problem is to know the velocity of the vertical end or > the CM of the ladder at any instant.? > Now my confusion is.... > How come the speeds of the two ends of the ladder are different as the > vertical end travels the same distance in same time as the base (or > bottom end) travels.?? > So technically speaking the speeds of the two ends must be the same?? > Then if we move the base with constant velocity why can't we assign > the same speed to the vertically sliding end?? If the velocity of one end is constant, the velocity of the other end certainly is not constant. The distance moved by the two ends is only the same if the angle with the ground changes from alpha to pi/2 - alpha. In this case the integral of speed wrt time is the same at both ends, but the instantaneous speeds are almost always different (they are equal only when the angle with the ground = pi/4). === Subject: minimum Hamming distance among random bit vectors Let p(b,n,d) be the probability that among a set of n ramdom vectors of b bits, there exists two distinct vectors which differ by at most d bits out of b. We restrict to integers such that b>0, n>0, 0<=d<=b Except for typo, we have: [1] p(b,1,d) = 0 [2] p(b,2,d) = sum C(b,j)/2^b with C(i,j) = i! / j! / (i-j)! j=0..d [3] p(b,2^b,d) = 1 [4] p(b,n+1,d) > p(b,n,d) or p(b,n+1,d) = p(b,n,d) = 1 (in other words: p grows with n, then becomes stationary with p=1) assuming n<=2^b [5] p(b,n,0) = 1 - prod (1 - j/2^b) j=0..n-1 assuming n>1 [6] p(b,n,b) = 1 assuming n>1 [7] p(b,n,d+1) > p(b,n,d) or p(b,n,d+1) = p(b,n,d) = 1 (in other words: p grows with d, then becomes stationary with p=1) So far I fail to find a workable technique to exactly compute p(n,b,d) in the general case. I wonder if in the domain 2 <= n <= 2^(b/3) a valid approximation could be: [8] p(b,n,d) =~ 1 - (1 - p(b,2,d))^(n(n-1)/2) I also fail to characterise N(b,d) = min(n such that p(b,n,d)=1) D(b,n) = min(d such that p(b,n,d)=1) (in other word: when it is impossible to find n vectors which all differ by at least d bits) Any idea or reference ? Fran.8dois Grieu Note: Followup-To is set to sci.crypt === Subject: Re: minimum Hamming distance among random bit vectors >Let p(b,n,d) be the probability that among a set of >n ramdom vectors of b bits, there exists two distinct >vectors which differ by at most d bits out of b. >We restrict to integers such that b>0, n>0, 0<=d<=b >Except for typo, we have: >[1] p(b,1,d) = 0 >[2] p(b,2,d) = sum C(b,j)/2^b with C(i,j) = i! / j! / (i-j)! > j=0..d >[3] p(b,2^b,d) = 1 >[4] p(b,n+1,d) > p(b,n,d) or p(b,n+1,d) = p(b,n,d) = 1 >(in other words: p grows with n, then becomes stationary with p=1) >assuming n<=2^b >[5] p(b,n,0) = 1 - prod (1 - j/2^b) > j=0..n-1 >assuming n>1 >[6] p(b,n,b) = 1 >assuming n>1 >[7] p(b,n,d+1) > p(b,n,d) or p(b,n,d+1) = p(b,n,d) = 1 >(in other words: p grows with d, then becomes stationary with p=1) >So far I fail to find a workable technique to exactly compute >p(n,b,d) in the general case. I wonder if in the domain >2 <= n <= 2^(b/3) a valid approximation could be: >[8] p(b,n,d) =~ 1 - (1 - p(b,2,d))^(n(n-1)/2) >I also fail to characterise > N(b,d) = min(n such that p(b,n,d)=1) > D(b,n) = min(d such that p(b,n,d)=1) >(in other word: when it is impossible to find n vectors which >all differ by at least d bits) If d is even, each bit vector occupies a space within d/2 of the bit vector. That's sum( b!/j!/(b-j)! ) j=0..d/2 So N(b,d) is at most 2^b / the above sum. --Keith Lewis klewis {at} mitre.org The above may not (yet) represent the opinions of my employer. === Subject: Closed form of x_(n+1)=r*x_n*(1-x_n) Hello My friend told me x_(n+1)=r*x_n*(1-x_n) behaved funny for certain values of r (for instance 3.9). Would be nice to find a closed formula. I tried Z transforms bu got st on the non-linearity. Then I tried to take the logarithm but got st on the sum Sum(log(1-x_n), n=0 to infinity) which I couldn't express in terms of sums of log(x_n). Is there maybe some online text about non-linear recursion? Is it maybe easy to say that there is no closed form of this sum? === Subject: Re: Closed form of x_(n+1)=r*x_n*(1-x_n) > Hello > My friend told me x_(n+1)=r*x_n*(1-x_n) behaved funny for certain values > of r (for instance 3.9). Would be nice to find a closed formula. I tried > Z transforms bu got st on the non-linearity. Then I tried to take the > logarithm but got st on the sum Sum(log(1-x_n), n=0 to infinity) > which I couldn't express in terms of sums of log(x_n). > Is there maybe some online text about non-linear recursion? Is it maybe > easy to say that there is no closed form of this sum? look up Feigenbaum constant. There is no closed form. === Subject: Re: Closed form of x_(n+1)=r*x_n*(1-x_n) > Hello > My friend told me x_(n+1)=r*x_n*(1-x_n) behaved funny for certain values > of r (for instance 3.9). Would be nice to find a closed formula. I tried > Z transforms bu got st on the non-linearity. I believe a closed form is known only for the cases r=0,2,4,-2 and no others. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Closed form of x_(n+1)=r*x_n*(1-x_n) Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) > Hello > My friend told me x_(n+1)=r*x_n*(1-x_n) behaved funny for certain values > of r (for instance 3.9). Would be nice to find a closed formula. I tried > Z transforms bu got st on the non-linearity. >I believe a closed form is known only for the cases r=0,2,4,-2 and no >others. Is there any indication that there might be impossibility thms here, i.e. for some values of r, you cannot have a closed form (with specified restrictions)? -- Mitch (remove the q for email) === Subject: Re: Closed form of x_(n+1)=r*x_n*(1-x_n) >Hello >My friend told me x_(n+1)=r*x_n*(1-x_n) behaved funny for certain values >of r (for instance 3.9). Would be nice to find a closed formula. I tried >Z transforms bu got st on the non-linearity. Then I tried to take the >logarithm but got st on the sum Sum(log(1-x_n), n=0 to infinity) >which I couldn't express in terms of sums of log(x_n). >Is there maybe some online text about non-linear recursion? Is it maybe >easy to say that there is no closed form of this sum? There is a *vast* amount of literature about this equation. It's called logistic map. Related topics are Feigenbaum number, chaos, fractals... (The term chaos came from a papaer about this equation: Period 3 implies chaos by Lie/Yorke). See http://mathworld.wolfram.com/LogisticMap.html http://en.wikipedia.org/wiki/Logistic_map There is no closed form solution for every r. I don't think it is easy to see. Non linear recursions generalize to discrete dynamical systems - a very rich mathematical theory. Hope, that gets you started. Thomas === Subject: Re: Periodic function >Your implied message is indeed very interesting! : < A Fourier >decomposition of a periodic wave need not be through sin cos >functions, but can be decomposed using ANY periodic function of same >period.> > I hope I didn't imply this: it's obviously not true that just because > f : R --> R is periodic (with period T, say) that you can conclude > the span of the family of functions f_n(x) = f(nx) will be dense in > (say) C([0,T]). After all, if you start only with the periodic > function f(x) = sin(x), all you can make as a sum of the f_n's will > be odd functions; you'll never get cos(x) that way. Or, even if > you begin only with the functions f(x) = sin(x) and g(x) = cos(x), > and then toss in the composites sin(nx) and cos(nx) with integer n, > you'll never get the function sin(x/2) --- even though both it and > the putative basis functions are all periodic on [0, 4pi]. > I don't know what it takes to ensure that a starting handful of > periodic functions will lead to basis. > But yes, it IS true that, while the functions sin(nx) and cos(nx) form an > orthogonal basis, they are certainly not the only basis one can use. > dave Yes indeed, I :)implied the usual Fourier decomposition modality viz., odd functions are synthesized using odd basis components, even functions from even components and others from the mixture, all with the new orthogonal basis. === Subject: Re: Schroedinger equation in wrong coordinates >Solving the Schroedinger equation for the hydrogen atom is relatively >simple after the early step of translating the equation from >Cartesiancoordinates to spherical coordinates which then allows a >straightforward separation of variables to give three simple (ish) >equations. But what I can`t seem to be able to find out is whether it is >actually possible to solve the equation using Cartesian >coordinates i.e. the x, y and z rather than the r, theta, phi. Now, I >appreciate that it might be madness to attempt such a feat when it is >relatively simple to go over to spherical coordinates, but I`d really >like to know if it is *theoretically possible* to solve it in Cartesian >coordinates. Can anyone say definitively whether it be done (if you were >a maths genius, for example)? >David. > Hi! > Changing coordinates is a change of language, so there must be > an unitary operator which performs the trick. If you care to find this > operator, then, starting from the solution in spherical coordinates, > you end up with the cartesian solution. Now, if what you want is to arrive > at the cartesian solution without using other coordinates even at intermediate > steps, this seems to me rather uninteresting. It is like trying to solve > a differential equation forbidding oneself to change variables. However, > it must be possible to do it (if I were a maths genius). > Best wishes, > G. I think you're closest to my understanding of the Ôdifficulty' satisfying the question directly. Whenever we Ôsolve' an equation, we're using Arithmetic. When we do so with differential equations, we do so along what they call Exact sequences, wherein the diferrential (or boundary) operator takes us from one integrable (ßat) space to the next. That is a geometrical feature of the solution to problem, which we cannot really wish away without also losing the ability to Ôsolve'. If one wants a Ôchange of coordinates' to ÔCartesian' just for the heck of it, I think there is an isomorphic transformation associated with Riemman, but I think Riemman attributed to Gauss: The stereographic projection. So the spherical problem can be turned into a ÔCartesian one' on the stereographic projection plane (say the equatorial plane). Problem is, the projection pole maps to infinity, so the minimal covering for it is two projections, say one rooted at the north pole excluding the north pole, and another rooted in the south pole, excluding the south pole, and with yet another change of coordinates to smoothly switch projections at their selected Ôoverlap' at say the equatorial plane. So given that atlas covering of the sphere, yes, there is a ÔCartesian' solution, but then you have to respect the Spherical geometry and thereby only deal with a Complex field. I do not know if this still meets the OP's requirements; but at last reading, the projection from spherical vector to ÔCartesian' used the transformation: (theta,rho,radius)-> (2^-2(x-iy),-z,-2^-2(x+iy)) All that Hermitian Vector space stuff... MK === Subject: Re: functions that halt In sci.math, |-|erc : > oo > ____|mn > / /_/ / _ - Herc, The Unrecognised Truman > / K-9/ /_/ - Join www.chatty.net - > /____/_____ - Nanotechnology is gonna be HUGE... (RMF) > -------------- > That wasn't my interpretation at all... it sounded like the author was >relating the countability/uncountability of a set with its property of >being listable (with a first element), which is entirely acceptable. > (But I do agree that asking what number comes next Ôafter pi' is kind of >irrelevant... as there will exist a one-to-one correspondence of a set >like the rationals with any rational at all after some given rational, >a/b. The only possible answers to his question were any real you want or >no real at all.) > O.K., I think I understand your interpretation now, and it seems plausible. > I retract my objection. > The objection was irrelevant, the next real after arctan(1)*4 might > be arctan(1)*5, Not horribly likely. Arctan(1)*4.5 would be right in the middle. Repeat indefinitely. :-) > it depends on the godel numbering system used, which admitedly > would have to be very clever to include all types of functions > and always halt. > Herc -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: functions that halt > That wasn't my interpretation at all... it sounded like the author was >relating the countability/uncountability of a set with its property of >being listable (with a first element), which is entirely acceptable. > (But I do agree that asking what number comes next Ôafter pi' is kind of >irrelevant... as there will exist a one-to-one correspondence of a set >like the rationals with any rational at all after some given rational, >a/b. The only possible answers to his question were any real you want or >no real at all.) > > O.K., I think I understand your interpretation now, and it seems plausible. > I retract my objection. > The objection was irrelevant, the next real after arctan(1)*4 might > be arctan(1)*5, > Not horribly likely. Arctan(1)*4.5 would be right in the middle. > Repeat indefinitely. :-) > it depends on the godel numbering system used, which admitedly > would have to be very clever to include all types of functions > and always halt. arctan(1)*4 = 3.141592.... I'm assuming we have a godel numbering system here, say arctan is symbol 10, ( is 11, ) is 12, * is 13... arctan(1)*4 10 11 1 12 13 4 say 10 is most significant and 4 is least significant, then the next highest expression one number higher than pi is 10 11 1 12 13 5 which is arctan(1)*5 Not sure where the divide and conquer gesture enters the hypothetical ordering here? Herc === Subject: Re: functions that halt In sci.logic, |-|erc : > That wasn't my interpretation at all... it sounded like the author was >relating the countability/uncountability of a set with its property of >being listable (with a first element), which is entirely acceptable. > (But I do agree that asking what number comes next Ôafter pi' is kind of >irrelevant... as there will exist a one-to-one correspondence of a set >like the rationals with any rational at all after some given rational, >a/b. The only possible answers to his question were any real you want or >no real at all.) > > O.K., I think I understand your interpretation now, and it seems plausible. > I retract my objection. > > The objection was irrelevant, the next real after arctan(1)*4 might > be arctan(1)*5, > Not horribly likely. Arctan(1)*4.5 would be right in the middle. > Repeat indefinitely. :-) > it depends on the godel numbering system used, which admitedly > would have to be very clever to include all types of functions > and always halt. > > arctan(1)*4 = 3.141592.... > I'm assuming we have a godel numbering system here, > say arctan is symbol 10, ( is 11, ) is 12, * is 13... > arctan(1)*4 > 10 11 1 12 13 4 > say 10 is most significant and 4 is least significant, then the next highest expression > one number higher than pi is > 10 11 1 12 13 5 > which is arctan(1)*5 > Not sure where the divide and conquer gesture enters the > hypothetical ordering here? Ah, OK. So what's 11 10 1 13 12 4 encode into? Oops. > Herc -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: functions that halt > That wasn't my interpretation at all... it sounded like the author was >relating the countability/uncountability of a set with its property of >being listable (with a first element), which is entirely acceptable. > (But I do agree that asking what number comes next Ôafter pi' is kind of >irrelevant... as there will exist a one-to-one correspondence of a set >like the rationals with any rational at all after some given rational, >a/b. The only possible answers to his question were any real you want or >no real at all.) > > O.K., I think I understand your interpretation now, and it seems plausible. > I retract my objection. > > The objection was irrelevant, the next real after arctan(1)*4 might > be arctan(1)*5, > > Not horribly likely. Arctan(1)*4.5 would be right in the middle. > > Repeat indefinitely. :-) > > it depends on the godel numbering system used, which admitedly > would have to be very clever to include all types of functions > and always halt. > > arctan(1)*4 = 3.141592.... > I'm assuming we have a godel numbering system here, > say arctan is symbol 10, ( is 11, ) is 12, * is 13... > arctan(1)*4 > 10 11 1 12 13 4 > say 10 is most significant and 4 is least significant, then the next highest expression > one number higher than pi is > 10 11 1 12 13 5 > which is arctan(1)*5 > Not sure where the divide and conquer gesture enters the > hypothetical ordering here? > Ah, OK. So what's 11 10 1 13 12 4 encode into? > Oops. ( arctan 1 * ) 4 One of those null functions, permissable since the emulator/computer still halts with null as output. Its only combinations that form infinite loops it must deny a godel number for. I've relaxed the countable definition to every function is enumerated from the more stringent 1:1 with N mapping, then we don't need to detect duplicate functions. Herc === Subject: Re: mass density In sci.math, Donald G. Shead > > (N = kg m/s/s so this works from a units standpoint. However, > most people would simply use kg/m^3.) > Now there's a crock for you: > The quantity of matter [m] in any body or mass can be expressed as > various ratios: > [m] = w/vol. = f/a = ft/(s/t) = ft^2/s = w/g > Then, by dimensional analysis'; we find from [m] = w/(vol), that w = > [m]/vol. and f = [m]/a = wa/g :: ... that > 1 newton = 1newton x a/(9.81 m/sec^2) ... _NOT_ N = 1 kg.87s-2!!! Actually 1 N would be your base unit. 1 kg = 1 N / (1 m/s/s). -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: mass density >Simply specifying units of density is meaningless: What in the world; >or the whole universe for that matter, has units of One kg/m^3? I'd >like to know! What in the world; or the whole universe for that matter, has a density of One lb/ft^3? I'd like to know! Gene Nygaard === Subject: Re: mass density >Simply specifying units of density is meaningless: What in the world; >or the whole universe for that matter, has units of One kg/m^3? I'd >like to know! > What in the world; or the whole universe for that matter, has a > density of One lb/ft^3? > I'd like to know! > Gene Nygaard Why do you care?? - Use the SI units and you still get a meter defined as the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second - AND a second is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. You are sooo far from finding a ratio of 1. Do you worry that you aren't the right height for your average weight or volume?? Maybe so (I do), but I don't call the units into question. === Subject: Re: mass density >Simply specifying units of density is meaningless: What in the world; >or the whole universe for that matter, has units of One kg/m^3? I'd >like to know! > What in the world; or the whole universe for that matter, has a > density of One lb/ft^3? > I'd like to know! > Gene Nygaard > Why do you care?? - Use the SI units and you still get a meter defined > as the length of the path traveled by light in vacuum during a time > interval of 1/299 792 458 of a second - AND a second is defined as the > duration of 9 192 631 770 periods of the radiation corresponding to the > transition between the two hyperfine levels of the ground state of the > cesium 133 atom. You are sooo far from finding a ratio of 1. > Do you worry that you aren't the right height for your average weight or > volume?? Maybe so (I do), but I don't call the units into question. Whoosh! === Subject: Problems with singletons I have a class Global that I use in several different places in my program. I only want a single instance of this object at any one time, because it allocates external resources. So I define a GlobalSingleton() function that returns a reference to a single Global object. Now I want to prevent myself from instantiating a Global() object within my program. I do this by declaring the constructor private. However, now the GlobalSingleton() function is not able to instantiate the object either. I would like to make the GlobalSingleton() a friend of the Global class, but I can't get the syntax to work. Any hints on how to proceed? -Michael. class Global { //friend GlobalSingleton; //private: Global(); public: void DoSomething(); } Global& GlobalSingleton() { static Global global; return global; } int main() { GlobalSingleton().DoSomething(); Global().DoSomething(); // Should not be allowed. } === Subject: Re: Problems with singletons > I have a class Global that I use in several different places in my program. > I only want a single instance of this object at any one time, because it > allocates external resources. So I define a GlobalSingleton() function that > returns a reference to a single Global object. > Now I want to prevent myself from instantiating a Global() object within my > program. I do this by declaring the constructor private. However, now the > GlobalSingleton() function is not able to instantiate the object either. I > would like to make the GlobalSingleton() a friend of the Global class, but I > can't get the syntax to work. > Any hints on how to proceed? > -Michael. // A somewhat inelegant suggestion: // Try asking in a C++ group if you want better. class Global { private: // prove an explicit copy constructor which does nothing. Global(Global &g) { throw An exception; } // this counts the number of objects created by the constructor. static int noOfObjects = 0; public: Global() { noOfObjects++; if(noOfObjects != 1) throw An Exception;} doSomething(); initGlobal(); // initiation should occur after you have constructed // your single object, so provide a method for it. } // create one instance with default values before you do anything else. globalObject = Global(); // this is not strictly necessary, but never mind Global& globalSingleton() { return globalObject; } int main() { // initiate the object: globalSingleton().initGlobal(); try { globalObject.doSomething(); // should work foo = new Global(); // this should throw an exception. } catch(...) { // whatever... } } -- P.A.C. Smith ÔMy duke of the blood royal [Gloucester] can beat up your duke of the blood royal [York], and you know it.' - Me, ars.userfriendly.org, 23/4/04 === Subject: Re: Help Needed Understanding Article Charlie-Boo schreef: > How about an example? Here's a couple of simple problems: . . . > You don't seem to understand Jasper at all. > I ask for an example and you conclude that I don't understand him? > How do you conclude that? Since I say you can't always generate programs automatically from a specification and you request me to do just that. > 1. I take it that you believe that the system that you describe can be > used to create computer programs from a specification that is not a > program, correct? What convinced you? Euh... this system is Coq, I think? Then the answer depends. Coq is not, unlike some other systems (e.g. Otter, and apparently the Boyer-Moore prover we started the thread with), an automatic theorem prover. This means it will not, automatically and all by itself, construct a proof for a theorem, i.e. a term for a type; i.e. a program for a specification. But even Coq has /some/ automation - there is, e.g., the Auto tactic. If the user types this in, Coq will try to generate a proof (program) anyway. Usually it fails though, and then the user has to do some additional work (i.e. programming). Also in Coq one may define their own tactics. These can be made rather strong and hence could also be seen as a kind of automatic proof search (i.e. program creation). Once a theorem is proved, its proof corresponds to a program. This is still in the Coq language (Gallina), but Coq can actually extract a compilable, runnable Haskell or OCaml program from it. > 2. Have you ever seen any examples of an actual program that was > generated? Yes. > 3. Can this system synthesize programs to meet the two requirements > (prime numbers and factor checking) that I asked for? How are these requirements? You mean can it implement these programs? Certainly. Although, as I said, this program synthesis will not be automatic - the user has to provide at least something. (Well - at least I don't suppose the Auto tactic is strong enough.) In a more conventional setting I suppose you might call that programming. Or at least providing the proof outline. > 4. If the answer to (2) or (3) is yes, then could you supply the > inputs (program specifications) and outputs (computer programs) as I > described in my previous post? (You can omit the proofs themselves if > that is too complex to present here.) Since it isn't that would be hard to do. But the input would be something like Require PolyList. Lemma primes_list : (k,n:nat){l:(list nat) | (m:nat)(In m l)<->(Between k n m)/(Prime m)}. ... ... ... Qed. assuming suitable definitions of Between and Prime, e.g. Definition Between [k,n,m:nat] := (lt k m)/(gt n m). Definition Prime [p:nat] := (k,n:nat) (mult k n)=p -> k=p/n=p. After this you apply the Extraction command and you have your prime list program. Jasper -- The problem with having an open mind is that people toss in garbage === Subject: Re: Help Needed Understanding Article > Charlie-Boo schreef: > How about an example? Here's a couple of simple problems: . . . > You don't seem to understand Jasper at all. > > I ask for an example and you conclude that I don't understand him? > How do you conclude that? > Since I say you can't always generate programs automatically from a > specification and you request me to do just that. Could you give me the actual quotes? So far it is a very broad statement without any substantiation. > 3. Can this system synthesize programs to meet the two requirements > (prime numbers and factor checking) that I asked for? > Since it isn't that would be hard to do. But the input would be > something like > Require PolyList. > Lemma primes_list : (k,n:nat){l:(list nat) | (m:nat)(In m l)<->(Between > k n m)/(Prime m)}. > ... > ... > ... > Qed. > Definition Between [k,n,m:nat] := (lt k m)/(gt n m). > Definition Prime [p:nat] := (k,n:nat) (mult k n)=p -> k=p/n=p. > After this you apply the Extraction command and you have your prime list > program. Could you fill in the rest, i.e., what goes in the . . . and what would the programs created be? And could you explain each line? (Some seem somewhat clear, but I want to be sure of how this Program Synthesis system works.) Charlie Volkstorf Cambridge, MA > Jasper === Subject: Re: Help Needed Understanding Article > 1. I take it that you believe that the system that you describe can be > used to create computer programs from a specification that is not a > program, correct? What convinced you? > 2. Have you ever seen any examples of an actual program that was > generated? Last two years I have been involved in a type theory course in which the students had to synthesize a sorting program and greatest common denominator function using Coq. The results of these projects where Haskell programs. The students had to do the proving part themselves, but in principle this could be taken over by a theorem prover (although any current automatic theorem prover will probably be too weak for any real applications). The course pages are still online at: http://www.phil.uu.nl/~oostrom/typ/xx-yy/ where xx-yy is 02-03 for sort, and 03-04 for gcd. The pages are in Dutch, sorry, but I think you're mainly interested in the source files. > Also note that I do NOT prove a proposition. I use a scheme that is > structurally the same as an axiomatic system (with axioms, rules of > inference and theorems), but it is a generalization of the notion of a > wff being true or provable. I show that the set or function involved > is recursive or recursively enumerable. The claim that something is r.e. is a proposition too. You use a different kind of logic, but you do use logic, and when glancing over I am not saying that your paper is not interesting, but your comments in this thread do suggest to me that it is not as revolutionary as you claim. But also non-revolutionary papers can be interesting. I will react to some quotes from the excerpts you posted. > It also doesn't seem to be formal. Expressions in set theory and > logic are well defined and represent formal concepts, of course, but I > don't see where they give a general scheme of exactly what can > constitute a specification and exactly how the various rules are > applied. It seems to be more intuitive. As mathematicians, we > understand what they are doing. However, software would need an exact > algorithm as to how these rules are chosen at each step and how they > are applied. What do you mean by formal? The above suggests to me that you require that a decision procedure can be defined, but maybe I misunderstand you. If you claim that your system *automatically* generates a program for *every* specification, then either your notion of specification is very weak, or there is somewhere an error in your logic. For any usable notion of specification, even determining whether a given program satisfies it is undecidable. > Also please note that I am not creating the program from an actual > proof. It is syntactically a proof, in that we are manipulating wffs > using rules of inference, but the semantics are not that the wffs are > true. The semantics are that we have a program that computes the > actual value of the wff (true or false in the case of wff P which has > no output variables.) You omit a predicate, indeed, but it is just different notation for something not fundamentally different. I would prefer using higher-order language, like R(P) instead of your P, and using inference rules like R(P) => R(~P). But okay, everyone may invent his own notations, if he wants. > 2. I have looked at Cog and I see no examples of a generated program. > It seems to be a high level programming language. It is calling it a > proof and there is mention of executing a proof. Whatever we call > it, the user is inputting a series of commands and they are executed. > This explains why there is no program to output. It is simply > executing what the user types in. The easiest way for a human to prove the formula is indeed to write a function and prove that it satisfies it. So the proving part in Coq is usually partly writing a program. But this is a practical issue, not a fundamental one. > It seems that in Cog the output would be prime numbers (not programs > that can be run to generate the prime numbers), assuming that Cog can > be used for such specifications. If I am wrong, then please let me > know. You're wrong. Coq will output programs. > My aim for many years has been to see who has done it, but nobody has > come up with an example of a program that any other system created. > That anyone would believe in a system without seeing any examples of > what it does is to me an astonishing achievement - of a BS artist. :) Even if someone accomplishes some scientific goal for the first time (and I am not saying you did), his work usually builds on related work of others. Claims like nobody did this before, their work is just bs often is a sign that someone finds his image more important than science. suggestions for improvement: * I see only proofs *in* your formal system, not *about* it. For example, I miss proof that: your system is consistent, it is sound, complete, that it does what you claim it does, etc. Examples are not enough. * Include references to other work on the same topic, even if you feel it is inferior to your own. Summarize the work in your paper, and write down why you think your system is better. * Make the paper look more professional (fix the font errors). Preferably, use some variant of TeX, e.g. LaTeX (it is the only system I know that produces high-quality mathematical text that is viewable on most platforms). groente -- Sander === Subject: Re: Help Needed Understanding Article > Last two years I have been involved in a type theory course in which the > students had to synthesize a sorting program and greatest common > denominator function using Coq. > The course pages are still online at: > http://www.phil.uu.nl/~oostrom/typ/xx-yy/ > where xx-yy is 02-03 for sort, and 03-04 for gcd. Not available. Could you just indicate the input required to create a program - any program? I studied Coq, and it is just a programming language. Give an example and I will show you what I mean. The system merely executes the commands as input. There is no one-to-many relationship between what is input and the program in another language. It is a one-for-one translation between two programming languages. Please give a specific example so that the viewers can see the truth. > Also note that I do NOT prove a proposition. I use a scheme that is > structurally the same as an axiomatic system (with axioms, rules of > inference and theorems), but it is a generalization of the notion of a > wff being true or provable. I show that the set or function involved > is recursive or recursively enumerable. > The claim that something is r.e. is a proposition too. You use a > different kind of logic, but you do use logic, and when glancing over Has there ever been any paper on Computer Science that did not contain some sort of logic and propositions? You are a very high level of abstraction, indeed. Too high to see the distinction that I am making. I do not prove the wff true. (It is not even a proposition except in the special case.) I prove the function or set recursive or recursively enumerable. Ordinary theorem-proving does not suffice. > 2. I have looked at Cog and I see no examples of a generated program. > It seems to be a high level programming language. It is calling it a > proof and there is mention of executing a proof. Whatever we call > it, the user is inputting a series of commands and they are executed. > This explains why there is no program to output. It is simply > executing what the user types in. > The easiest way for a human to prove the formula is indeed to write a > function and prove that it satisfies it. So the proving part in Coq is > usually partly writing a program. But this is a practical issue, not a > fundamental one. It is the basis of the system .9a and it is not Program Synthesis when the user has to write the program. Charlie Volkstorf Cambridge, MA > groente > -- Sander === === Subject: Re: Weight > ÔWarped'space is even more mysterious. Gravity force doesn't have to > be action_at_a_distance, just FTL. And why can't gravity simply propagate at c? The very first test of Special Relativity Theory was performed by Einstein himself in the very paper in which he proposed the theory. He was able to derive an expression that correctly determined the observed advance of the perihelion of Mercury. He assumed that the gravitational attraction between the Sun and Mercury propagates at c rather than with infinite speed. > Now you may want to reply and say > that nothing moves faster than c. That is is of course a postulate. More than that, it is the Principle of Relativity. > Do you know how fast electrons move in a copper undersea cable from NY > to London? Maybe a few mm per second. Sounds mysterious to you? Your patronizing tone is unbecoming. The value you provide refers to the bulk electron velocity under a small potential. The thermal velocity of individual electrons and the velocity of propagation of an electromagnetic wave through the medium of the metallic conduction band (the Fermi sea) are of course many orders of magnitude higher. > Even > if c is the limit you can still get almost action_at_a_distance Is almost action_at_a_distance anything like almost a virgin? It touching. > with a > space-time having the right features, like a copper wire does. All you > need is transmission of potential changes, not forces. Tell us what those features of space-time would be, O Wise One, that we may measure them and prove your theory. The current theory (that E-M energy is self-propagating) seems to work quite well, so we would need to be able to measure a difference between the consequences of current theory (which does not need an aether) and the aether theory. If there is no difference between the consequences of your aether theory and the Ôno aether' theory, then the aether would seem superßuous and the principle of parsimony alone would impel us to discard the aether. Tom Davidson Richmond, VA === Subject: Chain rule auxillary function(s)? Yo, When proving the chain rule the quotients [g(f(x))-g(f(x_0))]/[f(x)-f(x_0)] and [f(x)-f(x_0)]/(x-x_0) are replaced by auxillary functions, well always the first one by many authors do prefer to replace the second one too. Do they replace the second one because: (a)They think it looks more consistent, uniform or thst the end result looks better? (b)It is easy to generalize the method to more general cases, such as the vector case? or does it actually exist some strange domain where x can equal x_0 in some points when taking the limit. f(x) is usually defined on an interval of R. Isn't it just confusing to have two auxillary functions if you don't need it, right? / === Subject: Re: Chain rule auxillary function(s)? > When proving the chain rule the quotients > [g(f(x))-g(f(x_0))]/[f(x)-f(x_0)] and [f(x)-f(x_0)]/(x-x_0) are > replaced by auxillary functions, well always the first one by many > authors do prefer to replace the second one too. > Do they replace the second one because: > (a)They think it looks more consistent, uniform or thst the end result > looks better? > (b)It is easy to generalize the method to more general cases, such as > the vector case? > or does it actually exist some strange domain where x can equal x_0 in > some points when taking the limit. f(x) is usually defined on an > interval of R. > Isn't it just confusing to have two auxillary functions if you don't > need it, right? x = x0 is not what's happening. But [g(f(x))-g(f(x_0))]/[f(x)-f(x_0)] is still problematic. So you need some way to handle that; voila, auxillary functions. My opinion: the CR can be better proved without these things; they tend to confuse students. === Subject: Re: Chain rule auxillary function(s)? Adjunct Assistant Professor at the University of Montana. >Yo, >When proving the chain rule the quotients >[g(f(x))-g(f(x_0))]/[f(x)-f(x_0)] and [f(x)-f(x_0)]/(x-x_0) are >replaced by auxillary functions, well always the first one by many >authors do prefer to replace the second one too. >Do they replace the second one because: >(a)They think it looks more consistent, uniform or thst the end result >looks better? >(b)It is easy to generalize the method to more general cases, such as >the vector case? Neither. They replace it because while the second function is defined everywhere except at x_0, and therefore you can take limits as x goes to x_0, the first function is undefined everywhere that f(x) = f(x_0). This includes x_0, but may also include an infinite number of other points, arbitrarily close to x_0. When you talk about the limit of a function as x->x_0, you need the function to be defined everywhere near x_0, except perhaps at x_0; that is, there must exist some d>0 such that for all x, if 0<|x-x_0|or does it actually exist some strange domain where x can equal x_0 in >some points when taking the limit. f(x) is usually defined on an >interval of R. >Isn't it just confusing to have two auxillary functions if you don't >need it, right? You do need them. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Chain rule auxillary function(s)? by many in my original question should have been but many. and thst should be that Ok, We have the quotients [g(f(x))-g(f(x_0))]/[f(x)-f(x_0)] and [f(x)-f(x_0)]/(x-x_0) The first one MUST be replaced by an auxillary function because of the technical problem that the denominator can be zero in some points which can be arbitrarily close to x_0. I TOTALLY agree with this. My question is: The second quotient is often also replaced, by many of the most well known writers. Why is that? / === Subject: Re: Chain rule auxillary function(s)? > You do need them. No you don't. === Subject: Re: Chain rule auxillary function(s)? Adjunct Assistant Professor at the University of Montana. > You do need them. >No you don't. Sigh. You could do a completely different proof without using the function [gf(x)-gf(x_0)]/(f(x)-f(x_0)). But that was not the question (thank you for so kindly removing all context, by the way), your pedagogical preferences notwithstanding. The question was why you would introduce them AND NOT USE THE FUNCTION [gf(x)-gf(x_0)]/(f(x)-f(x_0)) directly. The answer is you cannot. If you are going to try to analyze that function with a limit as x->x_0 to reach the conclusion, you need to introduce an auxiliary function that takes care of the cases in which f(x) = f(x_0) but x is different from x_0. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Chain rule auxillary function(s)? > You do need them. > No you don't. > Sigh. You could do a completely different proof without using the > function [gf(x)-gf(x_0)]/(f(x)-f(x_0)). > But that was not the question (thank > you for so kindly removing all context, by the way), your pedagogical > preferences notwithstanding. > The question was why you would introduce them AND NOT USE THE FUNCTION > [gf(x)-gf(x_0)]/(f(x)-f(x_0)) directly. That was not the question at all. He was asking why some authors use a second auxillary function to handle [f(x)-f(x_0)]/(x-x_0), which does not suffer from the zero-denominator problem. Even if the first auxillary function is used, you don't need the second. So You do need them is wrong. Which means No you don't is right. === Subject: Re: Chain rule auxillary function(s)? Adjunct Assistant Professor at the University of Montana. > You do need them. > > No you don't. > Sigh. You could do a completely different proof without using the > function [gf(x)-gf(x_0)]/(f(x)-f(x_0)). > But that was not the question (thank > you for so kindly removing all context, by the way), your pedagogical > preferences notwithstanding. > The question was why you would introduce them AND NOT USE THE FUNCTION > [gf(x)-gf(x_0)]/(f(x)-f(x_0)) directly. >That was not the question at all. He was asking why some authors use a >second auxillary function to handle [f(x)-f(x_0)]/(x-x_0), Guess you're right. Had the context been left, it would have been easy for me to get the foot out of my mouth. So once again, thank you so very much for removing it in the first place. >which does not >suffer from the zero-denominator problem. Even if the first auxillary >function is used, you don't need the second. So You do need them is >wrong. Had the context been left, it would be clear that: (a) in the context of my reply, you do need them refered to replacing the first function: because while the second function is defined everywhere except at x_0, and therefore you can take limits as x goes to x_0, the first function is undefined everywhere that f(x) = f(x_0). So, the reply did not address the question. And the phrase, taken out of context, becomes wrong (as opposed to just immaterial). > Which means No you don't is right. Which means that no you don't is only right because you purposely misrepresented my (admittedly misguided) words. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: @.@ topology~ === Subject: Re: @.@ topology~ >show that >A<=>every infinite subset of A has an accumulation point in A. > If the space isn't first countable, there can be a sequence which > has an accumulation point but no convergent subsequence. >For example? >The example in Kelley, IIRC, is N x N where a neighbourhood of (0,0) >must contain all but finitely many members of all but finitely many >columns; all singletons other than (0,0) are open. Ah, Arens space. Turns out Arens space is Hausdorff and anti-compact, ie all compact sets are finite. Hence convergent sequences are eventually constant. >An enumeration of N x N is a sequence which has (0,0) as an >accumulation point. But any subsequence either has infinitely many >members in some column or at least one member in infinitely many >columns. Either way we can choose a neighbourhood of (0,0) that >misses infinitely many members of the subsequence, showing that the >subsequence does not converge to (0,0). Conversely if S is Hausdorff (or T1) and all converging sequences are eventually constant, is S anti-compact? Comment. 1st countable T1 space where all converging sequences are eventually constant is discrete, hence anti-compact. Same proof as 1st countable T1 anti-compact S ==> S discrete. If a not isolated: int {a} = nulset; S = cl Sa; some (aj)_j in Sa with aj -> a A = { aj, a | j in N } compact, finite; a in open U = S - Aa Aa / U = nulset which cannot be -- lower spaces When S is anti-compact, then all converging sequences are finite, ie { aj | j in N } is finite. Conversely ... what anti-compact, finitely almost discrete? Almost discrete is when space partitions into minimal open sets. Finitely so when each partition part is finite. ---- === Subject: Toronto space If X is a Hausdorff space of cardinality aleph_1 such that X is homeomorphic to any of its subspaces of cardinality aleph_1 then X must be discrete. Yes or no? ---- === Subject: Re: A question about continuous bijections from R2 to R2 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TEBuO20876; Suppose you want to show continuity of f^{-1} at point f(p). Choose a neighborhood W of f(p) which misses the complement of V, and a neighborhood B of p which maps into W. By choosing B with a smaller radius if necessary, we can assume that the closure of B is contained in U. If C is the closure of B, then f restricted to C is a homeomorphism, since C is compact, and everything is Hausdorff. Now I think that it follows that f^{-1} is continuous at f(p), as this is a local property at any rate. This is just a shot in the dark, so sorry if any or all of it is nonsense. Mark Motley >The problem is simple. Given a continuous bijection f from an open set >U to an open set V (the case where U, V are in R2 should be enough to >consider), is f-1 also continuous ? The answer is intuitively expected >to be negative. Indeed it is quite easy to find a counter-example when >the sets U and V are not supposed to be open ... but this is not the >problem stated. >So what happens when U and V are open sets ? === Subject: Re: A question about continuous bijections from R2 to R2 > Suppose you want to show continuity of f^{-1} at point f(p). Choose > a neighborhood W of f(p) which misses the complement of V, and a > neighborhood B of p which maps into W. By choosing B with a smaller > radius if necessary, we can assume that the closure of B is contained > in U. If C is the closure of B, then f restricted to C is a > homeomorphism, since C is compact, and everything is Hausdorff. Now I > think that it follows that f^{-1} is continuous at f(p), as this is a > local property at any rate. No, this does not work. You cannot deduce from this that f ^{-1} is continuous at f(p), because you have not proved that f(C) is a neighborhood of p. function from the reals endowed with the discrete metric into the reals endowed with the usual metric. But the inverse of that function is not continuous. Jose Carlos Santos === Subject: Re: f(x*y) = f(x) + f(y) >Hello >Suppose f is a function from the positive reals into R and satisfies >the functional equation f(x*y) = f(x) + f(y) for every x,y>0. If we >know that f(a) =1 for some a>0, then can we assure that f(x) = log >(x)? (here, log should be understood as referring to basis a). >It's easy to show that f(x) = log(x) for every rational x>0. > How do you do that? Actually, I assumed f is monotonic. If this is the case, f has an inverse g, and it's easy to show that g(u+v) = g(u)g(v) for every real u and v. Then, it's easy to conclude that g(r) = a^r for every rational r, which implies f(u) = log (u) (basis a) for every positive rational u. > Since the >positive rationals are dense in the positive reals, if we prove f is >continuous on (0, infinity), then we are done. But, I couldn't prove >that the functional equation f satisfies implies continuity. We also >see that if f is continuous on some x0, the f is continuous on its >whole domain. >I think if a>1 and one adds the assumption that f is increasing, then >it's continuous. And if to the original conditions one ads the >assumption that f is diffrentiable at some x0, then certainly f(x) = >log(x). >But based only on the original conditions, I'm not sure if we can say >f(x) = log(x). > Don't think you can. This is essentially the same problem as asking > whether any additive map from the reals to the reals must be > multiplication by a constant. > Make the positive reals into a vector space over > Q, by letting vector addition be multiplication and letting scalar > multiplication be exponentiation. > Clearly, any Q-linear map from the positive reals to the reals will > satisfy your condition f(u*v) = f(u)+f(v). > Pick your favorite a>0, different from 1 (note that f(1) must be 0, so > the a you had at the beginning was not equal to 1); now extend the set > {a} to a basis of the positive reals as a Q-vector space. Now we have > a whole host of maps that send a to 1 and extend linearly to all of > R^*, the logarithm base a being just one of them. > -- > It's not denial. I'm just very selective about > what I accept as reality. > --- Calvin (Calvin and Hobbes) > Arturo Magidin > magidin@math.berkeley.edu === Subject: Re: f(x*y) = f(x) + f(y) Adjunct Assistant Professor at the University of Montana. >Hello > >Suppose f is a function from the positive reals into R and satisfies >the functional equation f(x*y) = f(x) + f(y) for every x,y>0. If we >know that f(a) =1 for some a>0, then can we assure that f(x) = log >(x)? (here, log should be understood as referring to basis a). > >It's easy to show that f(x) = log(x) for every rational x>0. > How do you do that? >Actually, I assumed f is monotonic. If this is the case, f has an >inverse g, and it's easy to show that g(u+v) = g(u)g(v) for every real >u and v. Then, it's easy to conclude that g(r) = a^r for every >rational r, which implies f(u) = log (u) (basis a) for every positive >rational u. It is that last step I don't see. I can see how from g(r)=a^r you conclude that f(a^r) = r = log(a^r) for every rational r, but I don't see how you conclude that f(r) = log(r) for every rational u. Even assuming monotonic. Like it's been pointed out, taking g(x) = a^x and composing with your function f gives an additive function from R to R, f(g(x+y)) = f(a^{x+y}) = f(a^x*a^y) = f(a^x) + f(a^y) = f(g(x)) + f(g(y)). It is easy to see that in any additive function h:R->R rational number q you have h(q) = q*h(1). Here you have f(g(1))=f(a)=1, so that gives that f(a^q) = qf(a) = q for every q. And it is easy to verify as well that in general, your function will satisfy f( x^r) = rf(x) for every rational number r. But I simply do not see how you conclude that f(r) = log(r) for every rational number r. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: f(x*y) = f(x) + f(y) >Suppose f is a function from the positive reals into R and satisfies >the functional equation f(x*y) = f(x) + f(y) for every x,y>0. If we >know that f(a) =1 for some a>0, then can we assure that f(x) = log >(x)? (here, log should be understood as referring to basis a). > No, that's insufficient to imply f(x) = log(x). >I think if a>1 and one adds the assumption that f is increasing, then >it's continuous. And if to the original conditions one ads the >assumption that f is diffrentiable at some x0, then certainly f(x) = >log(x). >But based only on the original conditions, I'm not sure if we can say >f(x) = log(x). > Your intuition is quite correct. It is possible (with Choice) to construct > non-linear, discontinuous functions g(x) that satisfy g(x+y) = g(x)+g(y), > and then f(x) = g(log(x)) will satisfy your functional equation. It's > based on the concept of a Hamel basis. The idea is you can consider > R as an (infinite-dimensional) vector space over Q, and the additivity > constraint translates to linearity over Q, which is a much weaker > condition than linearity over R. > And it's true that as soon as you assume f is increasing, or differentiable > somewhere, or even measurable on any interval, then f has to be a logarithm. > -- Erick Could you please outline a proof for the cases where f is increasing or measurable? I could do it when we assume differentiability at some point of R, it's not hard. But if f is increasing,it's more complicated. I found the following proof, I think it's right. First, I showed that f(r) = log(r) for every rational r (log to a basis a>1). We know g(x) = log(x) is uniformly continuous on [k, infinity) for every k>0 (for it's derivative g'(x) = 1/(x*ln(a)) is bounded on [k, infinity)). Then, for every eps>0 there's d>0 such that f(r2) - f(r1) 0, which implies f is continuous on (k, infinity), because every x>0 is in [k, infinity) for 0Suppose f is a function from the positive reals into R and satisfies >the functional equation f(x*y) = f(x) + f(y) for every x,y>0. If we >know that f(a) =1 for some a>0, then can we assure that f(x) = log >(x)? (here, log should be understood as referring to basis a). > And it's true that as soon as you assume f is increasing, or differentiable > somewhere, or even measurable on any interval, then f has to be a logarithm. >Could you please outline a proof for the cases where f is increasing >or measurable? I could do it when we assume differentiability at some >point of R, it's not hard. It's more convenient to consider g(x) = f(exp(x)) from R to R, such that g(x+y) = g(x) + g(y). If g is measurable, then for some k > 0 there is a measurable set S of positive measure in which |g(x)| <= k. But then |g(x)| <= 2 k in S + S, which contains an interval. Since g(rx) = r g(x) for rationals r, we find that there is a constant c such that |g(x)| <= c |x| for all x. Since |g(x+y) - g(x)| = |g(y)| <= c |y|, this implies g is continuous. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: f(x*y) = f(x) + f(y) > It's more convenient to consider g(x) = f(exp(x)) from R to R, such that > g(x+y) = g(x) + g(y)... > Since g(rx) = r g(x) for rationals r... I can see this for natural numbers. Expanding to negative integers and rationals doesn't look obvious to me:-( === Subject: Re: f(x*y) = f(x) + f(y) > g(x+y) = g(x) + g(y)... > Since g(rx) = r g(x) for rationals r... > I can see this for natural numbers. Expanding to negative integers and > rationals doesn't look obvious to me:-( g(x)=g(n*(x/n))=n*g(x/n) Sorry for the noise. === Subject: Re: f(x*y) = f(x) + f(y) > It's more convenient to consider g(x) = f(exp(x)) from R to R, such that > g(x+y) = g(x) + g(y)... > Since g(rx) = r g(x) for rationals r... > I can see this for natural numbers. Expanding to negative integers and > rationals doesn't look obvious to me:-( For negative numbers: g(x)+g(-x) = g(x+(-x)) = g(0) and, therefore, g(-x) = g(0) - g(x) But I guess that g(0) = 0. How to prove it, though? === Subject: Re: f(x*y) = f(x) + f(y) > For negative numbers: > g(x)+g(-x) = g(x+(-x)) = g(0) > and, therefore, > g(-x) = g(0) - g(x) > But I guess that g(0) = 0. How to prove it, though? g(x+0)=g(x)+g(0)=g(x) Never mind for negatives, then:-) === Subject: Re: f(x*y) = f(x) + f(y) >Suppose f is a function from the positive reals into R and satisfies >the functional equation f(x*y) = f(x) + f(y) for every x,y>0. If we >know that f(a) =1 for some a>0, then can we assure that f(x) = log >(x)? (here, log should be understood as referring to basis a). >But based only on the original conditions, I'm not sure if we can say >f(x) = log(x). > Your intuition is quite correct. It is possible (with Choice) to construct > non-linear, discontinuous functions g(x) that satisfy g(x+y) = g(x)+g(y), > And it's true that as soon as you assume f is increasing, or differentiable > somewhere, or even measurable on any interval, then f has to be a logarithm. >Could you please outline a proof for the cases where f is increasing >or measurable? I could do it when we assume differentiability at some >point of R, it's not hard. My measure theory was never that good to begin with so I don't think I'm qualified to sketch it. I suspect you would be able to show (for the additive function) that all the level sets must have the same measure, which I guess somehow can contradict the function being measurable :). >But if f is increasing,it's more complicated. I found the following >proof, I think it's right. First, I showed that f(r) = log(r) for >every rational r (log to a basis a>1). We know g(x) = log(x) is >uniformly continuous on [k, infinity) for every k>0 (for it's >Is this right? It seems perfectly correct to me, but there is a simpler proof that only requires regular continuity of log(x). Just take any real x, bound it above by a decreasing sequence of rationals, and bound it below by an increasing sequence of rationals. By monotonicity the value of f(x) is squeezed between the two sequences of f values, which both converge to log(x). -- Erick === Subject: @.@ knock~ knock~ Excuse me~ sir~ May I come in? in the Euclid space E^n, for a fix vector u in E^n, define T_u : E^n -> E^n , T_u(v) = v+u (T_u is translation) 1) if u =/= 0 , T_u is not linear transformation. -------------------- easy by contraposition. -------------------- 2) show that ||T_u(v-w)|| = ||v-w|| (namely, distance of between v,w is invariable by translation T_u) -------------------- um...... i think......... T_u(v-w) = v-w+u and v-w norm is same ?? i can't show that. help me....please~ thank you sir~ === Subject: Re: @.@ knock~ knock~ > in the Euclid space E^n, > for a fix vector u in E^n, > define T_u : E^n -> E^n , T_u(v) = v+u > (T_u is translation) > 1) if u =/= 0 , T_u is not linear transformation. > -------------------- > easy by contraposition. > -------------------- > 2) show that ||T_u(v-w)|| = ||v-w|| > (namely, distance of between v,w is invariable by translation T_u) > -------------------- > um...... > i think......... > T_u(v-w) = v-w+u and v-w > norm is same ?? i can't show that. No, they do not need to have the same norm. Are you sure that you've asked the right question? Perhaps that the question was show that ||T_u(v) - T_u(w)|| = ||v - w||. Jose Carlos Santos === Subject: Asymptotic Lines on positive Gauss curvature surfaces. The following is about general validity of substitution in Alfred Gray's book to obtain zero normal curvature lines on surfaces. Presently, I have no access to the book: Gray,A., Modern Differential Geometry of Curves and Surfaces with Mathematica , Boca Raton, FL : CRC Press. When u,v denote parameterization along principal directions,it appears that the substitution u ->(p+q)/2, v ->(p-q)/2 on surface [(x,y,z)= f(u,v)] yields real asymptotic lines on all surfaces in R^3 with negative Gauss curvature K. I obtained proper asymptotic lines (kn =0) with cuspidal edges/lines of regression on Pseudosphere and Kuen surfaces of constant negative Gauss curvature K using this substitution. The procedure was applied to surfaces of revolution where positive and negative K occur together, as in Torus and Bellows examples below. Surprisingly,the resulting 3D plots indicate that Ôasymptotic' lines are possible on positive Gauss curvature surfaces as well. For the sphere, I obtain Viviani lines as asymptotic lines from Gray's definition.Parameterization is [cos(t)^2,cos(t)sin(t),sin(t)].On Figure 1-12, pp9 Struik's book, [Lectures on Classical Differential Geometry, 2nd Edition, 1961 ] the Figure of Eight Viviani line is depicted with slight inaccuracy, at a crucial point on the equator the line of intersection has a tangent parallel to z-axis whereas it ought to be equally inclined +/- Pi/4 to y- and z- axes. May be elsewhere on internet a Fig of 8 curve is available. Just as numbers once considered imaginary are now included within complex numbers, cannot the Gray's definition of an asymptotic line be valid even on K>0 surfaces? If so, what about identity of osculating/tangent planes? Struik gives the relation dv/du= +/- cos(v).i for imaginary asymptotic (and isotropic) lines. [Ch 2-8, Equn(8-2) pp87]. I would much appreciate your explanative indulgence on this topic I am trying to learn. The substitution was mentioned to me by Mark Sudduth [website http://www.coolphysics.com (not Confusing Physics Gibberish -------- Hypar Asympt Lines by Gray Substitution u=(p+q)/2 & v=(p-q)/2 > HalfSum,HalfDiff g1=ParametricPlot3D[{u+v,u-v, v u /5 },{u,-2,2},{v,-2,2},PlotPoints->{10,10}]; g2=ParametricPlot3D[{p,q, (p^2-q^2)/20 -.06},{p,-4,4},{q,-4,4},PlotPoints->{10,10}]; Show[g1,g2]; -------- Clear[u,v]; u=(p+q)/2 ; v=(p-q)/2 ; Viviani Temple > Lines of intersection sph/cyl thro' sphere axis(rad=1,u=lat,v=long) cyl(dia=1) generator x=Cos[u]Cos[v];y=Cos[u]Sin[v];z=Sin[u]; ParametricPlot3D[{x,y,z},{p,0, 2 Pi},{q,0,2 Pi}, PlotPoints->{19,19},Axes->None,Boxed->False]; ----- Clear[x,y,z,p,q,P,Q,a,b]; a=1.4; b=1; x[p_,q_]=(a+b Cos[p+q])Cos[p-q]; y[p_,q_]= (a+b Cos[p+q])Sin[p-q]; z[p_,q_]=b Sin[p+q]; Asymptotic lines on Torus ParametricPlot3D[{x[P,Q],y[P,Q],z[P,Q]}, {P,-Pi,Pi},{Q,-Pi,Pi},PlotPoints->{29,29}, ViewPoint->{-1,-1,4}]; -------- === Subject: Re: Test Message - DO NOT REPLY! by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TFfc320546; I couldn't keep myself from replying. === Subject: @.@ kernel~ hello.....doctor~ kernel of homomorphism is either 0 or entire. -------------------- which homomophism is satisfy that?? i want to know that. let me advice, please~ thank you very much. my time is A.M 0:50 good night ! === Subject: Names for two special (maximal and minimal?) quotient sets 1. Is there a standard name (e.g. identity quotient set or some such) for the quotient set Q=S/E such that the equivalence relation E is the identity function on set S (i.e. such that Q={{a}:a in S}? 2. How about for the quotient set Q=S/E such that E=SxS (i.e. such that Q={S})? === Subject: Re: Names for two special (maximal and minimal?) quotient sets Adjunct Assistant Professor at the University of Montana. >1. Is there a standard name (e.g. identity quotient set or some >such) for the quotient set Q=S/E such that the equivalence relation E >is the identity function on set S (i.e. such that Q={{a}:a in S}? >2. How about for the quotient set Q=S/E such that E=SxS (i.e. such >that Q={S})? In both cases, you are talking about the trivial quotients of S; the latter may be the total or zero quotient (since you get a singleton and have identified all of S), and the former is sometimes called the trivial quotient (since you are not really doing much). -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Fourier first 20 coefficients I have a problem with fourier transformation. Supposing I have a N x M (N and M are powers of 2) matrix with values ranging from 0..255 (yes, its a grayscale image) and I want to calculate the first 20 coefficients of the fourier transformation (FFT or DFP doesn't matter because I only want the first 20). In simple words (and/or Borland Delphi code :):):) )what are the equations I can use? A form like: F1= F2= etc would be GREATLY appreciated:):) Marios === Subject: Re: Fourier first 20 coefficients >I have a problem with fourier transformation. >Supposing I have a N x M (N and M are powers of 2) matrix with values >ranging from 0..255 (yes, its a grayscale image) and I want to calculate the >first 20 coefficients of the fourier transformation (FFT or DFP doesn't >matter because I only want the first 20). >In simple words (and/or Borland Delphi code :):):) )what are the equations I >can use? >A form like: >F1= >F2= >etc would be GREATLY appreciated:):) Sorry, it has to be a form more like F1:= F2:= or it won't compile. (Seriously: do you know what the Fourier transform _is_? If not then why do you want to do this calculation?) === Subject: Re: Statistical question (discrete uniform sum distribution?) >What is the meaning of C(n,m) when n is negative? This must go back to Newton, at least. For non-negative n, C(n,m) is a polynomial in n of degree m (it is zero for m negative). Just use the same polynomial. With this convention, Newton showed (algebraically, i believe) that (1+x)^n = sum C(n,m) x^m, for |x| < 1. This is also what one gets when a Maclaurin series is used. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >I am trying to do a simulation study on random vectors having >multivariate normal distribution N(Mu, S). Suppose the generalized >variance (the determinant of the covariance matrix det(S)) is 1. I am >looking for a distribution of mean that would cover a wide range of >applications and concentrate on the most important ones (maybe with >the mean of |Mu| equaling to a specific number). Anyone has any idea There is no problem whatever in simulating from any given multivariate normal distribution; in fact, if S = AA', Mu + AZ, where Z is a vector of independent N(0, 1) random variables does this. If you want a prior distribution for Mu, this is a different question. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 > I am trying to do a simulation study on random vectors having > multivariate normal distribution N(Mu, S). Suppose the generalized > variance (the determinant of the covariance matrix det(S)) is 1. I am > looking for a distribution of mean that would cover a wide range of > applications and concentrate on the most important ones (maybe with > the mean of |Mu| equaling to a specific number). Anyone has any idea > You do not give enough information to advise you sensibly. > What is the purpose of the simulation? You know, of course, that you > can transform any normal distribution to have mean 0 and variance 1 > (i.e., the main diagonal of S is (1,1,...)) without loss of generality. > The mean vector plays a very minor role in all of this. It is far more > interesting to simulate S properly. Depending on your purposes, > there are a number of different things you can try. > Sorry for not giving enough information. I am comparing two > classifiers. Suppose we have data from two multivariate normal > distribution, N(Mu_1, S_1) for class 1 and N(Mu_2, S_2) for class 2. I > want to show that one classifier beats the other one (has a smaller > classification error rate) when (Mu_1, S_1, Mu_2, S_2) has a certain > distribution F. What I am looking for is a distribution F that > concentrates on the most popular (Mu_1, S_1, Mu_2, S_2). I am > considering the following transformations. > 1. Transform the data so that det(S_1) = 1, in this case, what are the > most possible |Mu_1|, |Mu_2| and det(S_2)? > 2. Transform the data so that Mu_1 = 0 and det(S_1) = 1, then Mu_2 > will be the difference between two centers. Now what are the most > possible |Mu_2| and det(S_2)? > 3. Do simultaneous reduction so that Mu_1 = 0, S_1 = I, S_2 is a > diagonal matrix. Then Mu_2 will be a linear transformation of the > difference between two centers, the diagonal elements of S_2 will be > the generalized eigenvalues of S_1 and S_2. Then what are the most > possible |Mu_2| and diagonal elements of S_2. This is harder than the > previous ones since a linear transformation is introduced. I still don't understand what you want to do. 3. is impossible in general. There is no guarantee that you can diagonalize S1 and S2 simultaneously. I do not know how much prior knowledge you have. What you want to do is called discriminant analysis in multivariate statistics. Typical discriminant functions are linear or quadratic. These are maximum likelihood methods, so in some sense they are optimal. Have you identified some weakness in the usual approach to discriminant analysis? Do you have some particular area of application in mind? Maybe you should take this to sci.stat.*. > Anyway, considering |Mu_1|, |Mu_2|, det(S1), det(S2) is my approach to > reach a distribution F that will concentrate on the most popular > (Mu_1, S_1, Mu_2, S_2). It may not be a good choice to find a > popular distribution F. Any advice will be highly appreciated. ath: nntpswitch.com === Subject: Re: Order type of English names of natural numbers >|> When counting, the next number after 999,999 is usually >|> referred to as one million, but expressing that >|> number, it can be said as just million. >| No. When writing a check, you write one million and never just >| million. >Well, check writing is another kettle of fish, and I was NOT referring >to ONLY checking writing. People do refer to (say) $1,000,000 as a >million dollars, and not always as one million dollars. As a matter of >fact, I didn't mention check writing at all. I did say, it CAN be >said as ... yada yada yada. One will say a million dollars but never just million dollars. Wheras one might say four dollars but never a four dollars. I think million in the sense of a million is being used as the same kind of word as dozen. Not exactly a number, I'm not sure what you call it. George >one hundred and two and 74/100 (dollars), but one hundred two and 74/100 >---this is the American way of spelling out (dollar) numbers on >checks --- as opposed to the British way of spelling 102 as >one hundred and two. You'll rarely hear a banker or cashier use two >ands when saying a dollar amount. But there are a lot of variants >of course, on both sides of the pond. __________________________Gerard S. === Subject: Re: Order type of English names of natural numbers >What about if we use standard binary numerals? >as in 1 < 10 < 100 < 1000 < ... < 1001 < 101 < 1010 < 10100 < ... ? > [...] >Then from this is should be easy to see that the order type is >omega^omega. er.. or is it 2^omega ? > But it isn't a well-ordering, is it? It seems there are infinite > decreasing chains such as > 101 > 1001 > 10001 > 100001 > 1000001 > ... Ah. Yes. I should haver seen that coming from the tree description; there are an infinite number of paths to either side of any given path So I misstated the lexicographic ordering because it is definitely a well-ordering. Here is the formal definition: for a words x and y, of lengths n and m respectively, x < y if: x is a proper prefix of y (that is n < m, and for all i <= n, x(i)=y(i)) or after an initial shared prefix of x and y, x has a 0 and y has a 1 (that is x = w0.* and y = w1.*, that is there's an i such that for all j The number you have posited is defective. > right here: > | | > one hundred twenty-five billion fifty-three million one thousand four > trillion trillion trillion trillion trillion trillion sixteen. What's defective about that? People have suggested quadrillion and similar higher-than-trillion terms, but if you go with that suggestion, then the defect is larger than the portion you indicated. I would suggest writing each triplet of digits separately, rather than having trillion trillion trillion trillion trillion trillion show up and modify the entire ten-digit sequence before it. So, instead of (one hundred twenty-five billion fifty-three million one thousand four) TTTTTT sixteen we would write (one hundred twenty-five billion TTTTTT) (fifty-three million TTTTTT) (one thousand TTTTTT) (four TTTTTT) sixteen [except with parentheses removed - they're just to show how the parsing works - and with each TTTTTT expanded to the full verbiage] === Subject: Re: Order type of English names of natural numbers Originator: tchow@lagrange.mit.edu.mit.edu (Timothy Chow) >I would suggest writing each triplet of digits separately, rather >than having trillion trillion trillion trillion trillion trillion >show up and modify the entire ten-digit sequence before it. So, >instead of >(one hundred twenty-five billion fifty-three million one thousand >four) TTTTTT sixteen >we would write >(one hundred twenty-five billion TTTTTT) (fifty-three million TTTTTT) > (one thousand TTTTTT) (four TTTTTT) sixteen Thinking about it some more, I agree with you...this seems to make more sense. Either way we have to cope with my infinite decreasing chain: two T two > two TT two > two TTT two > two TTTT two > .... However, if trillion is replaced by zillion as Stewart Gargis suggested, this one breaks down. I'll have to think more carefully about whether his proposed solution is correct in this case. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Order type of English names of natural numbers >I think it doesn't matter much whether you use and, the British >way (101=one hundred and one), or omit it, the US way (101= >one hundred one). It does make some difference though: the British >list will have > 102 one hundred and two >100000 one hundred thousand >whereas the US list will have >100000 one hundred thousand > 102 one hundred two > This will make some difference to the exact order in which the numbers > appear, but will it make a difference to the order *type*? (Two totally > ordered sets have the same order type if there is a one-to-one and onto > order-preserving correspondence between them.) Ah, so (A,B,C,D,E) and (1,2,3,4,5) have the same order type but also (A,B,C,D,E) and (A,B,D,C,E) have the same order type. But an ordering of aleph-zero elements and an ordering of aleph-one elements can't have the same order type, because no bijection can be constructed. Oof, I smell an Axiom of Choice tarpit ahead. === Subject: Re: Order type of English names of natural numbers > There is also the number: > asankhyeyu 10**140 1 followed by 140 zeros OY! Foul! If we are going to introduce the plethora of Indian numbers, there are plenty of special cases before that! There's the kalpa, 4320 000 000, whose one thousandth part is the mahayuga, 4320 000, which in turn divides into 4 with 4:3:2:1 ratio, Kaliyuda, 432000 Drapavay, 864000 Tretayuga, 1296000 Kutayuga, 1728000, all of which have some religious significance, naturally! Anyway, asankhyeyu sounds less like a number than a Japanese gentleman saying I thank you! ------------------------------------------------------------- ------------- -- -- Bill Taylor W.Taylor@math.canterbury.ac.nz ------------------------------------------------------------- ------------- -- -- Western philosopher on 1st contact with Indian culture:- Is EVERYTHING sacred!? ------------------------------------------------------------- ------------- -- -- === Subject: Re: Unmeasurable set and axiom of choice >Hi... >So far, all examples of unmeasurable sets I've encountered so far rely >on the axiom of choice for their existence. Is this true in general? >In other words, can we construct an unmeasurable set without using the >axiom of choice? For simplicity, we can assume a Lebesgue measure. Assuming the Axiom of Constructability is consistent, or equivalently the existence of measurable cardinals, the answer is no, as from AC above one gets that all subsets are Lebesgue measurable. There are sets in this model which are not Borel measurable. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: How to generate a covariance matrix S uniformly on det(S) = 1? >Does anyone know how to generate a covariance matrix S uniformly on >det(S) = 1? Any help is appreciated. > Covariance matrices are positive semidefinite, and are > definite with probability 1 if there are as many degrees > of freedom as the size. I have no idea what a uniform > distribution could possibly be on these. >I am looking for an algorithm to generate an p-by-p covariace matrix S >with density function of S as > Indicator(det(S) = 1) >p(S) = -------------------------------------------------- > The intergral of {Indicator(det(S) = 1)} >So the case where det(S) = 0 is automatically excluded. Integral with respect to what measure? The covariance matrices with det(S) = 1 forms a rather large subset of the set of non-singular covariance matrices. In fact, if T is a positive definite matrix, the matrix S = T/(det(T))^1/n has determinants 1. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Order type of English names of natural numbers by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TI6oQ24151; >If you prefer, use the system in Conway and Guy's The Book of >Numbers. >Does that change the answer? Yes. That naming scheme uses billibillion for 10^6009, billibillibillion for 10^6006009, and so forth. So there is no next number after eight, since you can say eight billibillibillibillibilli... until they lock you up. Dan Hoey haoyuep@aol.com === Subject: Are powers of 2 known to be the only minimally deficient numbers? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TI6qV24218; . Are powers of two known to be the only minimally deficient numbers? Mathworld says sigma(n) = 2n-1 iff n is a power of two, but elsewhere I saw this referred to as not proven. Can anyone clarify? Mark Griffith === Subject: Re: A proof for Goldbach's conjecture by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TI6qt24228; Breath taking. === Subject: Re: A Variation On Continued Fractions > Let x, a positive real, be represented as: > /a(0),a(1),a(2),a(3),.../, > which is short-hand for: > x = a(0)*(1 + 1/(a(1)*(1 + 1/(a(2)*(1 +...))))). > Now this may seem arbitrary at first. > But if we calculate a possible set of positive integer a()'s using a > Greedy-like algorithm, this representation may seem more natural. > For x >= 1, > Let a(0) = ßoor(x). > Let, with x(0) = x; > x(m) = 1/(x(m-1)/a(m-1) -1) > and > a(m) = ßoor(x(m)) > for all positive integers m (until, if ever, a(m) = x(m)). > Now, with some x's, anyway, there is more than one representation (set > of a's) which gets a particular x. > For one thing, letting a(0) =b(0), a(m) = b(m)b(m-1), for m = positive > integers, > always works, where b(k) is the k_th term in the simple continued > fraction of x. > But with x = pi, using the term-calculation algorith above, we get: > pi = /3,21,111,.../, > but 7*15 = b(1)*b(2) = 105, not 111. > But sometimes, a given x has the same representation, whether the a's > are calculated using the above algorithm or we have a(m) = b(m)b(m-1). > An example (probably the best example) of this is > x = (sqrt(5)+1)/2, which is > /1,1,1,1,1,1,.../. > In any case, which x's have different representations and which x's > have the same representation, whether calculated using the algorithm > or by having > a(m) = b(m)b(m-1)? > And what are such expansions, using the algorithm, of some well-known > constants? I should note that we can use this to transform sequences of positive integers into other sequences of positive integers. If we have the positive integer sequence {b(k)}, we can get x = the continued fraction [b(0);b(1),b(2),...]. And then we can use the recursive algorithm above to get the sequence {a(k)}, where x = /a(0),a(1),a(2),.../. (And in some cases, each a(m) {for m >= 1} is b(m)b(m-1), while in other cases the terms differ from b(m)b(m-1).) Leroy Quet === Subject: primitive root by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3TIaa502558; how can we prove that if p==1(mod 4) then principal squareroot of a == a^ (p+1)/4 === Subject: Re: primitive root Adjunct Assistant Professor at the University of Montana. >how can we prove that if p==1(mod 4) then principal squareroot of a == a^ (p+1)/4 By proving that the square of a^{(p+1)/4} is congruent to a modulo p. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu