mm-3909 === angle makes sense only in a real inner product space. If you have a complex inner product, then its real part is a real inner product, which can be used (for some purposes) to define angles in complex inner product spaces. -- http://www.math.ohio-state.edu/~edgar/ === Subject: Re: ? complex dot product If E is the projection on span(a), you can compute ||b-Eb||, or equivalently ||(I-E)b||, where I-E is the projection on span(a)^{perp}. There is a well known approximation problem: let W be a subspace of an inner product space V and v a vector in V; how do we choose w in W such that it is the best approximation to v? We choose w = Ev, where E is the projection on W. In this case we measure a distance, not an angle, but it's general. For instance, V could be C^{nxn} and the above would still be valid. Kiuhnm === Subject: Re: ? complex dot product How are you defining dot(a,b)? With or without involving complex conjugation somewhere? === Subject: Re: ? complex dot product Yes, with complex conjugate. But unless a and b are complex conjugate, its dot product remains a complex number. by Cheng Cosine Apr/20/2k7 NC === Subject: Re: Number Theory problem: seeking Calculus example My last message on this topic says the following: I first want to mention that both of these papers I had planned to submit are now submitted. I had planned to submit them last fall, but I did not get around to submitting them until a few weeks ago. I have also found new examples of nice polynomials with four roots (the roots and critical points are ordinary integers) with a computer. I have verified existence of examples of all degrees from 5 to 9 with all possible combinations of multiplicities and have verified existence of degree 10 with combinations 7,1,1,1; 6,2,1,1; and 5,3,1,1 of multiplicities. I plan to finish checking all possible combinations of multiplicities of degree 10 as soon as possible. Jonathan Groves === Subject: Compact vs Hausdorff The recent thread continuous bijections from X to X prompted me to look back at an older post (above) in which first James Dolan and then Dave Rusin provide some really cool insights into the competitive nature of the two topological properties compact and Hausdorff. So here's a belated followup question. Let X be a nonempty set and T a topology on X. Prove or disprove: (1) If (X,T) is compact but not Hausdorff, then there exists a finer (stronger) topology T' such that (X,T') is both compact and Hausdorff. (2) If (X,T) is Hausdorff but not compact, then there exists a coarser (weaker) topology T' such that (X,T') is both compact and Hausdorff. If X is finite, (1) is obviously true since you can refine T to the discrete topology, thus gaining the Hausdorff property while retaining compactness. Also, if X is finite, (2) is vacuously true. Hence if there is a counterexample to either (1) or (2), X must be infinite. Proofs or counterexamples? quasi === Subject: Re: Compact vs Hausdorff I believe these are both false. (X,T) compact such that no strictly finer topology is compact is a *maximal compact* topology. And similarly for *minimal Hausdorff* ... probably you can find these terms in the literature. -- http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Compact vs Hausdorff You may enjoy the book by Steen & Seebach, Counterexamples in Topology. http://en.wikipedia.org/wiki/Counterexamples_in_Topology -- === Subject: Re: Compact vs Hausdorff So I guess that means my questions might be answered in that book. If so, sorry, I didn't realize. quasi === Subject: Re: Call for Papers: WORLDCOMP'07, Las Vegas, June 25-28, Conferences in Computer Science, Computer Engineering, and Applied Computing One of the so-called sponsors is a lab at MIT. They better know how to use SCIgen. -C === Subject: Re: Call for Papers: WORLDCOMP'07, Las Vegas, June 25-28, Conferences in Computer Science, Computer Engineering, and Applied Computing Too late, the speaker has already crossed the river Styx. === Subject: Re: Call for Papers: WORLDCOMP'07, Las Vegas, June 25-28, Conferences in Computer Science, Computer Engineering, and Applied Computing Reminds the famous Interplanetary Chess Congress http://www.sovlit.com/chess.html === Subject: Re: Maple vs. Mathematica .. Hi Carlos, *exactly* this is the reason, why it is important to keep track of the difference between local and global variables. This is a very common error in programming. Sorry to say: The bug is mostly close to the keyboard/screen (have made bad experiences too). Peter === Subject: Re: Maple vs. Mathematica Absolutely correct. The x set to one should have been declared local to the module where was set, to avoid name space contamination. Sophomore students in an engineering major have virtually no idea of scope, however, since they typically begin programming in the freshman year with GUI front ends like excel, labview, or solidworks. It is interesting that Mathematica selected global as the default type, which is a serious design mistake. At least Fortran, with all its warts, got that right when subroutines were specified for FORTRAN II (August 1957, that is almost 50 years ago!). It might have be an inadvertent goof since I think that the ancestor of Mathermatica (a Caltech code, what was the name?) didnt have modules or blocks. === Subject: Re: Maple vs. Mathematica SMP, Symbolic Manipulation Program http://en.wikipedia.org/wiki/Symbolic_Manipulation_Program ... Well, here is a very early design document for SMP, written in the first couple of weeks of the project. http://www.stephenwolfram.com/publications/talks/specialfunctions/ === Subject: Moving a point in N-dim space Hi all, I have a question as follows Suppose a point in a N-dim space where all coordinations are positive integers, it can move along one dimension only towards the origin at one time slot. Given the moving distances along each direction are random integers following some PMF. The goal is to move such a point back to the origin while incurring as small as number of movements within a given T slots. It is also possible that we can not move back to the origin until T-th slot subject to the random moving distances. However, we want to control such failure probability to be less than some constant c. Moreover, notice that, when the moving distance along every direction are not large enough and the deadline is far away, the point may prefer to stay there for that slot in order to save steps. === Subject: Re: Comprehensive Solution Manual for Textbooks I am interested in getting the complete solutions manual for Elementary Number Theory - Kenneth H. Rosen (5th edition) (ISBN: 0321237072). I was wondering how long it is going to take till i get it and what the payment procedure is. I need it soon though === Subject: Re: Comprehensive Solution Manual for Textbooks I would like to request the answers for the book Fraud Examination - Steve Albrecht (2nd edition) (ISBN: 0324651155). And could you send me some sample or preview of the solution manual ? === Subject: Re: Thousands of solutions manuals http://rapidshare.com/files/26915061/Fundamentals_of_Electric_Circuits__2nd. ed.__by_C.K.Alexander_M.N.O.Sadiku__Solution_.rar === Subject: HUNDREDS AND HUNDREDS OF SOLUTIONS Contact bwennny@hotmail.com if interested. A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein A First Course In Probability 7th Ed by Sheldon Ross Adaptive Control 2nd Ed. by Karl.J.Astrom Advanced Engineering Marhematics ERWIN KREYSZIG 9E Advanced Engineering Mathematics 8Ed Erwin Kreyszig Advanced Engineering Mathematics 8Ed Erwin Kreyszig in korean (all even and odd no.) 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Phule (Instructor's Manual) Theory and Applications of OFDM and CDMA Wideband Wireless Communications (2005) Thermodynamic 5th ed. Cengal Thermodynamics: An Engineering Approach 5th Ed. by Cengel Boles (Instructor's Solutions Manual) Time-Harmonic Electromagnetic Fields by Harrington solutions, 2001 Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas Vol 1 Thomas' Calculus Early transcendentals 10th Ed. by George B. Thomas Vol 2 Transport Phenomena 2nd Ed. by Bird and Stewart(to class 1 and class 2 problems) University Physics with Modern Physics (11th) by Hugh D. Young and Roger A. Freedman. Vector Calculus 3rd Ed. by Susan Jane Colley Vector Mechanics for engineers dynamics by beer 6th edition Vector Mechanics for engineers dynamics by beer 7th edition Vector Mechanics for engineers statics by beer 6th edition Vector Mechanics for engineers statics by beer 7th edition (nearly the same with edtion 8) Wireless Communications principles and practice 2nd Ed. by Theodore Rappaport 1996 === Subject: A Question on Complex Numbers Prove that tan(pi/15) is a root of the equation t^3-6(sqrt(3))t^3+8t^2+2(sqrt(3))t-1=0 Give the other roots in the form tan(rpi/15), where r is a number. I've tried using the tangent identities of multiple angles (eg. tan5x=...) to solve the question, but with no success. Pls help. === Subject: Re: A Question on Complex Numbers Sorry...I made a mistake in the question. The equation should be t^4-6(sqrt(3))t^3+8t^2+2(sqrt(3))t-1=0. Also, the question requires the use of a trigonometric identity of a tangent of a multiple angle found using De Moivre's Theorem, and we cannot solve it as a quartic. === Subject: Re: A Question on Complex Numbers I don't quite understand. - Are these last points hints that you were given? If yes, here are some additions: You are looking for an algebraic equation that the value t := tan(phi), phi = Pi/15, satisfies. First ask yourself whether there is some multiple of phi for which you can easily calculate the tangent. - That's easy: 5*phi = Pi/3 with tan(5*phi) = sqrt(3). Now expand this equations in terms of t = tan(phi). - You obtain a polynomial equation of degree 5, not 4: 5*t-10*t^3+t^5-sqrt(3)+10*sqrt(3)*t^2-5*sqrt(3)*t^4 = 0 Don't be bothered by the wrong degree: *If* t really also satisfies some quartic equation, then there must be an easy linear factor contained in this quintic. So ask yourself: What other roots does this quintic equation have? In other words: What other solutions phi' are there for the equation tan(5*phi') = tan(5*phi), because for every such solution, tan(phi') will also satisfy the quintic. One of these (basically four) other solutions is phi'=2*Pi/3; so tan(2*Pi/3) = -sqrt(3) is a root of the quintic, and you can factor the quintic by (t-(-sqrt(3))) and obtain the quartic equation you are looking for: t^4-6*sqrt(3)*t^3+8*t^2+2*sqrt(3)*t-1 = 0. === Subject: Re: A Question on Complex Numbers To prove it is a root, just do substitution. let x=tan (pi/15) and if x^3-6(sqrt(3))x^3+8x^2+2(sqrt(3))x-1=0 , then it is a root. If it is a root, then polynomial divide the equation by (t- tan (pi/ 15) ) and you have a quadratic. Try factoring, or the Quadratic Formula. === Subject: Re: A Question on Complex Numbers Very blunt. Almost as blunt: set x^3-6(sqrt(3))x^3+8x^2+2(sqrt(3))x-1 = k_1 (x - tan(k_2 * pi/15)) * (x - tan(k_3 * pi/15)) * (x - tan(k_4 * pi/15)) You can do this because the range of tan is R, and hence any number can be expressed as tan(k*pi/15) for some k. Expand, and equate co-efficients. If k_1=1, then tan(pi/15) is a root; k_2 and k_3 give the values of r for the other roots. Dunno if this is easier than polynomial division, or even whether it will work at all. There has to be a *much* easier way ... === Subject: Win 50K INR- Participate in InfoQuiz 2007 Hi Participate in the Online InfoQuiz 2007 organized by International School of Information Management, India. Win upto 50K INR. Prizes sponsered by Rediff. Free Registration. to Register visit http://www.isim.ac.in Vikram === Subject: College students confused about manifolds with boundary Wikipedia claims that manifold with boundary is a manifold with an edge. For example a sheet of paper with rounded corners is a 2- manifold with a 1-dimensional boundary. The edge of an n-manifold is an (n-1)-manifold. A disk (circle plus interior) is a 2-manifold with boundary. Its boundary is a circle, a 1-manifold. A ball (sphere plus interior) is a 3-manifold with boundary. Its boundary is a sphere, a 2- manifold. By this definition, an empty sphere and an empty torus are not manifolds with boundary (since they don't have an edge). What about a punctured sphere (i.e. - sphere less the north pole)? I guess it has a boundary that is a point, which is two dimensions smaller. Does the boundary necessarily need to be an (n-1) manifold, or can it be an (n-2) manifold? Kind of unrelated, but is a punctured sphere orientable? We're not really sure what the hole does to this. GD & IC === Subject: Re: College students confused about manifolds with boundary Well, most people would say that every manifold is a manifold with boundary; specifically the boundary is empty. Of course the empty sphere and empty torus (that's a new one for me) are the same manifold, the empty manifold; and the convention is to regard it as an n-manifold for every n. That's why what I said above makes sense. A punctured S^n is homeomorphic to R^n, so it's a manifold with empty boundary. To make S^n into a manifold with nonempty boundary, remove an open disk. Then what you have left is a closed n-disk, which is a manifold with boundary. The boundary always has dimension n-1. This is a consequence of the definitions in terms of charts that look like half spaces. In the case of the n-disk, the boundary is (homeomorphic to) an (n-1)-sphere. Yes, see above: it's homeomorphic to R^n. -dave === Subject: Re: College students confused about manifolds with boundary A more precise definition is this: An n-manifold (without boundary) is a space in which every point has a neighborhood homeomorphic to R^n. An n-manifold with boundary is a space in which every point has a neighborhood homeomorphic either to 0 }. So a manifold looks locally like R^n. A manifold with boundary looks locally like R^n or half of it (in which case you are on the boundary). By these definitions, the empty set is a manifold, with or without boundary, of any dimension; the definition is vacuously satisfied because there are no points. A punctured sphere is a manifold without boundary. Any point is some positive distance from the hole, so you can choose a neighborhood which is so small that it stays away from the hole and thus can look like R^n. A *closed* disk (such as { z in C : |z| <= 1 } )is a manifold with boundary. An open disk (such as { z in C : |z| < 1 }) is a manifold without boundary. The Wikipedia entry is misleading in that respect. It can be shown that the boundary of an n-manifold with boundary is an n-1-manifold without boundary. Yes, it is. One way to think of orientability is to put at each point a unit vector which is perpendicular to the surface (pointing in or out). If you can do this in such a way that the vector field varies continuously (i.e. no sudden jumps), the surface is orientable. Now you can certainly do this for the sphere, or the punctured sphere, for example by having all the vectors point toward the center. In fact, removing points can never make an oriented manifold non- orientable. If you had a continuous perpendicular vector field, taking away some of the points (and their corresponding vectors) will not introduce jumps that weren't there before. The reverse, however, is possible, since removing points could remove jumps. For instance, the Mobius strip is not orientable, but remove a chunk (i.e. cut it open) and you have a plain old strip which is certainly orientable. Excellent questions! It's refreshing to hear from people who are genuinely curious about mathematics. === Subject: Re: College students confused about manifolds with boundary Very interesting. Is the boundary of a manifold the same as that which is represented by the partial differential symbol? Are manifolds with boundaries always compact? Please give a definition of compact, with an example, because accumulating points don't make any sense to me. Freiddie http://freiddy.blogspot.com/ http://crazibe.blogspot.com/ === Subject: Re: College students confused about manifolds with boundary Yes. No. For any topological space that is a subset of some R^n (with the topology it gets from R^n), compact is equivalent to closed and bounded. (If you don't know what closed is in this context, you should go back and learn that before you try to do much more with manifolds.) The interval { x in R : x is greater than or equal to 0} is closed (because it includes its only real endpoint, 0) and not bounded (because it is not included in any real closed interval [a,b]), so it is not compact; it is a 1-dimensional manifold-with-boundary, and its boundary is the non-empty 0-dimensional manifold {0}. In this case, the boundary happens to be compact. If you consider a half-plane in R^2 (all the points of some straight line, together with all the points on one side of the line and none of the points on the other side), they you have a non-compact 2-dimensional manifold-with-boundary, and its boundary is also a non-compact manifold (the line). === Subject: Re: Is language a mess? (was: English is a mess.) You have not even the beginnings of an inkling what entropy is. Best stay with linguistics until you have calculus, chemistry, physical chemistry, mechanics, electromagnetism, advanced mechanics, advanced electromagnetism, thermodynamics, quantum theory, and statistical mechanics. You may, if you wish, continue to dupe the wine and cheese crowd. -- Michael Press === Subject: Re: Is language a mess? (was: English is a mess.) I learned all I need to know about entropy from Isaac Asimov 40-odd years ago. In this instance, it refers to the evening out of energy -- the loss of Shannonian information -- over time. Gravitation, however, is not the image someone was going for. === Subject: Re: Is language a mess? So she couldn't even write her own name by the time she was 4? You're going to need a different anecdote to support your silly notion. === Subject: Re: Is language a mess? (was: English is a mess.) Only that it's never happened. Do tell us what you're referring to! Only that it's never happened. (Except in the first Tarzan book.) Do try to explain yourself. What, pray tell, is a paleolith, and what, pray tell, the hell are you talking about? Do, pray tell, identify some of them for me, and explain why I, who have been studying writing for some thirty years, have never come across one.. If they were doing that 2000 years ago, then -- even if somehow they'd managed to lose the skill -- their language families would have reconstructable words in that semantic field. There is, of course, no PIE word for 'write' or 'read'. === Subject: Re: Is language a mess? (was: English is a mess.) When did we stop talking about humans and start talking about animals? Feeding sheltering etc. a baby isn't teaching it something. Under what sense of behavior is survival a behavior? I think the Chomsky hierarchy has something to do with formal grammars, that he posited in the early 50s when he was still a mathematician? === Subject: Re: Is language a mess? (was: English is a mess.) A not-altogether-unreasonable reference: http://en.wikipedia.org/wiki/Chomsky_hierarchy Type 2 is the interesting type, from my perspective. Type 3 gets a lot of attention in some circles, but really, what's the point when you get so much more from type 2, and you have so many parsing algorithms to choose from? I suppose type 0 could also be considered interesting in that it's (I believe) computationally complete, but it's a pretty poor formalism in which to study computability. I don't really know much about Chomsky himself. Politically he seems like a crank. The universal grammar idea does not seem unreasonable, although I'm unclear whether there is any empirical way to verify it. Meh; natural language is not my field. Anyway, his contributions to formal language are clear. Marshall === Subject: Re: Is language a mess? (was: English is a mess.) Teaching very definitely is involved. The teaching may consist merely of indications of accuracy, or the pointing out of things and naming them, or other such hints. There is quite a bit else they do. They need to improve their walking to the point of stability, they need to learn how to recognize faces at different angles, they need to learn where they are allowed to go and where not, how to drink from a cup, how to use a spoon, etc. -- 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: Is language a mess? (was: English is a mess.) Did you never have children of your own? Or was their infancy so long ago that you have no memory of how their linguistic behavior changed over the months they were acquiring it? It is simply untrue that indicating accuracy leads a child to produce e.g. the correct irregular inflections. Once again, any psycholinguistics 101 textbook will include dialogs between adult and child where you can see how it works. Naming things, once again, is utterly irrelevant to the linguistic system. Have you ever heard of Piaget? === Subject: Re: Is language a mess? (was: English is a mess.) An enormous amount of their language is never explicitly taught to children, largely because the vast majority of parents aren't even consciously aware of the various intricacies of their language that they take for granted. For example, no ordinary parent teaches their children the peculiar semantics of the progressive aspect of stative verbs or the differences in subcategorization in verb pairs like eat/devour, look/watch, give/donate, etc. Further, there is plenty of research on language acquisition that shows that direct teaching has little or no significant effect on acquisition. In fact, direct teaching is often found to be counter-productive, causing confusion and/or frustration for the child. These facts are part of most ordinary introductory courses and texts in linguistics and developmental psychology. Nathan -- Nathan Sanders Linguistics Program Williams College http://wso.williams.edu/~nsanders/ === Subject: Re: Is language a mess? (was: English is a mess.) Because you're playing around with the word grow. === Subject: Re: Is language a mess? (was: English is a mess.) Show me how I'm playing around with the word grow. Better still, show me why (i) is natural but (ii) is artificial. === Subject: Re: Is language a mess? (was: English is a mess.) The growing that a plant does has no similarity whatsoever to whatever you intended by writing as a behavior grew. Since I don't know what you intended, I can't tell you what it has to do with your natural/ artificial dichotomy. === Subject: Re: Is language a mess? (was: English is a mess.) Have you ever watched an infant acquire language? Absolutely no teaching is involved, and absolutely nothing resembling what is done in school. Infants are language-acquiring-machines. It's just about the only thing they do for a couple of years. === Subject: Re: Is language a mess? (was: English is a mess.) Yup. Both functional and dysfunctional. Is teaching a requirement for learning to be going on? It isn't in the conventional sense of the word. But again, perhaps you are using a special linguistics-specific definition of the term. Heh! I'd assert that you left out the ever-popular vomiting and pooping, but that's a side issue. Also a side issue is that I think you are using the term infant a bit broadly; I wouldn't call an 18 month old an infant. Yes, infants are language-acquiring machines, but parents are also language-transmitting machines. They use simpler grammar and higher pitch with infants, not necessarily for conscious reasons. Does this behavior have any point *other* than to facilitate language acquisition in infants? Is it an instinct? The fact that the same behavior occurs with pet owners, especially owners of infantilized pets, suggests so. I am not asking rhetorically; as a specialist in this field you may have a different theoretical explanation for these phenomena than my naive one. Marshall === Subject: Re: Is language a mess? (was: English is a mess.) An infant, < Lat. in-fans, is a human that does not speak. It turns out that so-called Motherese is (a) an illusion and (b) far from a human universal. There are cultures that make no effort to speak more simply or clearly to infants, and the infants acquire their language on exactly the same timetable as our infants do. We don't have to worry about theory until the facts are accurate. === Subject: Re: Is language a mess? (was: English is a mess.) Peter T. Daniels: How will you do that without a theory about what constitutes accuracy? JSL. === Subject: Re: Is language a mess? (was: English is a mess.) We're hardly talking about minute quibbles here. We're talking about perfectly obvious macro-level facts that anyone who knows anything about the topic is familiar with. === Subject: Re: Is language a mess? (was: English is a mess.) Your is argument from authority. The OP is correct, and from a strictly scientific POV. Do you have an answer to the question? Tom === Subject: Re: Is language a mess? On 18 Apr 2007 12:01:43 -0700, Marshall sci.lang,alt.philosophy,sci.math: It's considerably more than a mere 'no': my point is that the question was asinine in the first place. To the best of my knowledge, there are no deaf *societies* without speech; I include the various sign languages as speech, of course. [...] === Subject: Re: Is language a mess? Hmm. Well, I would say you have not succeeded in adequately supporting that point. Still, I suppose the question is moot, since the initial issue was whether writing is natural or not, which, absent some specific definition of natural and some reason why we should care about it, isn't of much interest. Of course. :-) Marshall === Subject: Re: Is language a mess? On 18 Apr 2007 18:36:41 -0700, Marshall in sci.lang,alt.philosophy,sci.math: [...] Why the smiley? If you don't understand why they're speech, just say so. Brian === Subject: Re: Is language a mess? I beg your pardon for the misunderstanding. The smiley was not ironic, at least not in your direction. I was intending to make a reference to the fact that there has been some disagreement in this thread about what, exactly, constitutes language. That you and I apparently agree on this point warranted a smile, to me at least. As an aside, I must say you are quite a prodigious poster! (I checked your profile to make sure I was correct in my assumption that you're a native of sci.lang rather than sci.math or alt.philosophy.) I'm very impressed! Marshall === Subject: Re: Is language a mess? On 19 Apr 2007 10:51:35 -0700, Marshall in sci.lang,alt.philosophy,sci.math: Ah, my apologies. I fear that I'm a little more irritable than usual these days: we're approaching the end of the semester, so life is more than usually hectic, and my teaching schedule this term is ... unenviable. Chalk it up to an almost non-existent social life! I used to frequent sci.math -- I am a mathematician by education and profession -- but I got fed up with the anti-Cantor cranks, the 0.999... != 1 cranks, and the idiots whose response to the latter show that *they* don't understand that rigorously assigning meaning to a non-terminating decimal is non-trivial. Unfortunately, I usually found it impossible to ignore them. Brian === Subject: Re: Is language a mess? I've been thinking about where speech ends and non-speech communication begins. For instance, in the dark, sign language communication would be harder but fluorescence or phosphorescence could help. Somehow, ants, bees and termites coordinate their activities. In humans, people can tell lies, but fail to be convincing because of how they look and carry themselves. So I'd be interested to know what linguists mean when they talk about speech, in their jargon. David Bernier === Subject: Re: Is language a mess? The question is no more asinine than that of how intelligent beings elsewhere in the universe would communicate. Are the various sign languages in any way speech? Or are they more like writing in a very transient medium? If, as many claim, writing started by recording pictorial representations, and was only later extended to representing speech, it becomes very natural. -- 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: Is language a mess? It is the most natural thing to mark the passing of days, with the consequent necessity of grouping tally marks then rectifying them with the motion of the moon and seasons. Before you know it you are making calendars and doing mathematics, without ever, necessarily, recording spoken language. :-) -- Michael Press === Subject: Re: Is language a mess? Would you PLEASE learn something about a topic before you write more nonsense about it? This is a lot worse than your bs about ancient Egyptian, since it's not at all unlikely that you will someday encounter a deaf student or colleage at Purdue. Of course signed languages aren't in the slightes like writing; they do not represent some other language; they are languages identical in every essential property with spoken languages, differing only in mode. What does recording pictorial representations mean, and what does it have to do with signed languages? === Subject: Re: Is language a mess? sci.lang,alt.philosophy,sci.math: [Attribution restored:] This is an unnecessary nuisance; we can follow the attributions (if you keep all of them, as you should). Nothing relevant to Herman's ridiculous claim. Brian === Subject: Re: Is language a mess? Here we have an example of someone who could speak and communicate by speaking still coming up unaided from observation of others writing that there was communication by writing, and that she could attempt it. My claim is that it is possible to observe the use of written language by children and deduce the existence of that as a means of communication, which the child could learn to use. The contrary claim is that this is impossible; a proof of impossibility is very difficult, and in mathematics, to show possibility requires only one example. There are possible flaws in this example, but the flaws in the claim that a child COULD NOT learn to use a written language from seeing others use it are far more serious. -- 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: Is language a mess? No, that a particular blob of squiggles had a referent. You cannot observe the use of written language by children who have not been taught to use written language. People have been writing for a bit more than 5000 years, and there has never been an example of a child picking up the practice without being explicitly taught. === Subject: Re: Is language a mess? Writing would have been primitive at the start, but nonetheless, someone must have started writing something at some point, without being taught to do so. Possible evolution of writing? 1) Painting a picture of a bison is not writing but nonetheless does convey information. 2) Drawing a diagram (say of a group of stickman figures holding spears and surrounding a bison) conveys more information but, arguably, is not a form of writing. 3) Painting a sequence of diagrams would be a HUGE leap forward in the ability to convey information, and I would say is a form of writing. 4) Chinese picture writing *is writing* and uses one picture for each word in the language. w.r.t phonetic languages: I have just been reading up on cuneiform. The Sumerians' writing system later evolved into ideograms, which are symbols representing an idea without expressing a certain word or phrase for it. Ideograms greatly simplified the Sumerian writing system by allowing one sign to represent several different things. For example, a star symbol could mean sky, heaven, or god. Eventually the Sumerian system involved the phonetic use of signs, which made it possible to convey abstract ideas. Scribes began using signs to represent sounds. For instance, the symbol for water could be used to represent the word in (which is hard to express as a picture) because the two words sounded alike. In short, Cuneiform evolved as a shortened form of picture writing. The Cuneiform system of writing developed over a period of 500 years and evolved into about 2000 word symbols. By 3000 B.C.E, the Sumerians had developed a full system of Getting back to the issue: At sometime, someone started using signs to represent sounds without being taught to do so, and thus written phonetic language was born. Yes! It would not have been a child who did it. But someone did it without being taught. And thus writing developed naturally. === Subject: Re: Is language a mess? It wasn't a child who did so! The evolution of writing can be followed in the archeological record from virtually the very beginning, in Uruk ca. 3300 BCE. There is no need for speculation. true (though you'd do better to refer to pictograms rather than paintings) more in quantity, but perhaps not more in quality true (Of course, we don't know what your definition of writing is. Mine is A system of more or less permanent marks used to represent an utterance in such a way that it can be recovered more or less exactly without the intervention of the utterer. I don't remember where I first published it, but I've repeated it in just about every piece on writing I've ever published.) define diagram define sequence define writing Pure myth. A tiny raction of Chinese characters (5% or so) have a pictorial origin. The vast majority of Chinese characters combine an indicator of their semantics with an indicator of their pronunciation. Again, your unpreparedness for this discussion is apparent. Please learn some basic facts. What is a phonetic language? who or what is richeast.org? later after what? simplified it from what? I'm afraid Mr. East, or whoever this is, knows nothing about Sumerian writing. Hardly any of the assertions in that paragraph is factually accurate. See, at the very least, the contributions by Michalowski and Cooper in *The World's Writing Systems*, edited by me and William Bright. define 'naturally' === Subject: Re: Is language a mess? Are you willing to admit a second independent invention of writing in the New World by the Mayas and their predecessors? Independent invention in China is also possible, but so is stimulus diffusion from Sumer. Chronologically the New World might also be stimulus diffusion, but how such diffusion could have occurred boggles my mind === Subject: Re: Is language a mess? You've never read a word I've published. I am de'sole'. Stimulus diffusion from Sumer to China is _not_ an option. However, the evolution of writing cannot be followed in the archeological record from virtually the very beginning in either China or the New World. === Subject: Re: Is language a mess? On 19 Apr 2007 07:20:33 -0700, Peter T. Daniels in sci.lang,alt.philosophy,sci.math: [...] Rich East High School, Park Forest, Illinois. The web page is 'The Evolution of Cuneiform'; according to the notation at the foot of the page, '[t]his web page was was written by T.N.and T.D.H., March 19,1998, for History & Thought of Western Man, Rich East High School'. [...] Brian === Subject: Re: Is language a mess? Sheesh. You'd think anyone from a Chicago suburb would have gone on either a class field trip to the Oriental Institute, or been taken there by their parents, where they could have learned some true facts either from the docents or from the carefully age-graded materials available to all visitors. === Subject: Re: Is language a mess? But perhaps relevant to Peter's claim, which was: Unlike to speak, no infant will automatically learn to write just by observing people around it writing. === Subject: Re: Is language a mess? Oh -- if your daughter was unable to speak by the age of 4, she was very special indeed. === Subject: Re: Is language a mess? Nothing you said about your daughter indicates she had the slightest understanding of what writing is or how it works. She was able to recognize a particular blob of squiggles as referring to herself. Nothing more. === Subject: Re: Is language a mess? On 18 Apr 2007 12:04:10 -0700, Jens S. Larsen sci.lang,alt.philosophy,sci.math: [...] Why on earth should it? [...] Brian === Subject: Re: Is language a mess? (was: English is a mess.) So then you would be saying: Behaviors which are gene-driven are natural (if plants growing could be said to be a behavior) and behaviors which aren't gene-driven are artificial. Is it even possible to determine whether some particular human behavior is gene-driven or not? (1) Perhaps those default assumptions need to be looked at once in a while. (2) For the purpose of picking an hypothesis: Ockham's razor. Entities should not be multiplied needlessly. In this case, the entities would be the stuff needed for a child to start with and still learn one of our human languages. Is a capacity to learn enough? or is a universal, innate underlying language required? Neither. Just me and my little brain puzzling this out for myself. But I can't say whether Pinker or Locke had an influence on the training in philosophy and linguistics that I did receive. Can you give me a few examples of such words? AFAICS, the question comes down to this: === Subject: Re: Is language a mess? (was: English is a mess.) Scot: Growth is easy enough. They are. I don't think neurologists would get far if they gave up the modular mind now. If parrots can learn to imitate speech, how come you can't have a conversation with them? Well, the mind as a blank slate is Locke's expression and the title of Pinker's book... There, it, is, of, to... typically those small words that don't get translated between English and Chinese. Jens S. Larsen === Subject: Re: Is language a mess? (was: English is a mess.) Did you miss the point accidently, or purposefully? How about the question of whether language is gene-driven and whether writing is gene-driven? But finally it dawns upon me that we are talking about a nature vs nurture argument. Clearly we aren't going to get much further on this topic. Imitating speech is not speech. And diversion away from the issue isn't discussion of the issue. ^ Pinker, Steven. The Blank Slate. New York: Penguin. 2002. page 346-350. For example, boys surgically reassigned as girls in infancy and raised as girls spontaneously self-identify as boys. Back to that nature vs nurture argument. Clearly there is something on the slate w.r.t. sexual identity. But can anyone prove what is on the slate w.r.t. language? I think you just gave me a hint: If those small words are used for the construction of sentences in one language but not another then they are not part of any underlying universal language or universal underlying grammar. That implies that any rich structure is NOT innate. === Subject: Re: Is language a mess? (was: English is a mess.) Scot: Yes and no respectively. Language is an organ that grows, just like teeth and for similar genetic reasons. Reading and writing are activities that result from purposeful combination of natural capacities, one of which is language. Great progress is being made these days, though. Then we have two mental modules already: one for imitation, one for speech. Perhaps the assumptions behind the issue need to be looked at once in a while. There's a whole science dedicated to the question. It's called linguistics. However, progress in this science is somewhat hampered by many of its practioners' deeply felt hostility to theorizing. Then you must provide an answer to the question: How do Chinese children learn their language _without_ such words in the input from the environment? They need a single structure that works both for the English and for the Chinese system. Otherwise we all must have one brain area for learning English, another one for learning Chinese, and so on for all languages past, present and future. Jens S. Larsen === Subject: Re: Is language a mess? (was: English is a mess.) [Here's the analogy:] In a neural network simulation on a computer (which might not be a valid model at all for how a brain really works), the network has a structure (layers of neurons) but other than that the network work starts out as a blank slate. A computer neural network can be trained to recognize a simple language (set of inputs and outputs). The structure of the network makes this possible but there was no underlying language already encoded before training started. [and here's the conclusion:] The structure of the brain allows it to learn English or Chinese (or both) but that doesn't mean that it had an underlying language coded on there from the start. === Subject: Re: Is language a mess? (was: English is a mess.) Completely linguistically naive neural networks fail on anything with even moderate linguistic complexity. Invariably, some amount of pre-existing linguistic knowledge has to be encoded into the network in order to get them to function correctly. Pre-existing linguistic knowledge is comparable to Jens's underlying language, differing primarily in extent. Nathan -- Nathan Sanders Linguistics Program Williams College http://wso.williams.edu/~nsanders/ === Subject: Re: Is language a mess? (was: English is a mess.) Interesting! But I would not consider this to be persuasive evidence in the direction of underlying language. The situation is adequately explained by the comparatively poor computational power of existing neural networks relative to a human infant. However it certainly merits further study. As an aside, please note that I have no objections to the underlying language hypothesis. In fact I find the idea appealing, although note also that I do not consider that it appeals to me to have any particular significance. Marshall === Subject: Re: Is language a mess? (was: English is a mess.) You should ignore Jens's somewhat idiosyncratic use of underlying language. Chomsky is not representative of all of linguistics, and even for Chomskyans, the question of precisely what linguistic knowledge is pre-specified in the human brain is hardly settled. It can range from the strong (essentially a full syntactic grammar from the outset) to the weak (a relatively small set of options that languages make use of). Either way, Jens's use of underlying language is misleading. Even the most extreme Chomskyans don't believe that Universal Grammar is a viable language in its own right, with a fully determined phonology, morphology, semantics, and pragmatics. It may very well turn out that human language acquisition can be reduced to a general learning algorithm with no need for pre-specified linguistic knowledge. Current neural networks and similar models can't do it, though. Until suitable models are constructed, linguistics marches on, trying to find out what pre-specified linguistic knowledge seems to be required. It's a constant back and forth: find some seemingly universal linguistic principle, then keep chipping away anything that can be derived from general cognition, and when/if there's nothing left, start over with a new linguistic principle. I'm not expecting any useful convergence on this matter in my lifetime, but I'd be happy to be wrong about that! Nathan -- Nathan Sanders Linguistics Program Williams College http://wso.williams.edu/~nsanders/ === Subject: Re: Is language a mess? (was: English is a mess.) Accounts for his style that moves from vagueness, agnosticism, and avowed disinterest to dogmatic assertion and back, as easily as a pike slips through the weeds. Arguing with them is a mug's game. -- Michael Press === Subject: Re: Is language a mess? (was: English is a mess.) I think it's Ray Jackendoff who has most clearly shown that the neural network model isn't adequate to model language acquisition or use. === Subject: Re: Is language a mess? (was: English is a mess.) How could writing be gene-driven? How could the human brain have evolved a particular writing-capacity in 5000 years, when literate populations don't reproduce in preference to non-literate populations? What survival value would writing have? What does prove mean in brain/cognitive science? instantiate it. === Subject: Re: Is language a mess? (was: English is a mess.) Good question. Do the humanities bother with falsifiability? Science is supposed to be falsifiable. === Subject: Re: Is language a mess? (was: English is a mess.) So observational sciences like astronomy -- are not sciences, because they're not Popperian? Linguistics, obviously, is an observational science, since there are as yet no tools for investigating brain operation on a level of any useful sort of fineness. You can probe individual neurons in animal brains, but those pesky folks on ethics committees don't allow that to be done in people, and only people can talk. === Subject: Re: Is language a mess? (was: English is a mess.) Theories of astronomy are most certainly faslifiable. Astronomers do not make inductive conclusions from their data sets. How does your idea of scientific linguistics compare? Tom === Subject: Re: Is language a mess? (was: English is a mess.) Observations ar falsifiable. I think linguistics, when it deals with the observable, is falsifiable but may not have much in the way of predictive value. Regardless of predictive value, I think observable linguistics is still worthwhile. I think it was Jens who said that studying languages (ie.. the observable stuff) has no scientific value. And Jens said the only scientific value is in studying language ie. the underlying, universal language. But in my opinion, that supposed underlying, universal language isn't falsifiable. I don't know if any such theories would have any predictive value either. I fail to see the point of talking about an underlying universal language. === Subject: Re: Is language a mess? (was: English is a mess.) I'll leave it to Jens to advocate his own Chomskyan position. === Subject: Re: Is language a mess? (was: English is a mess.) A language is what the users of that language collectively decide it is. Desiderata on the part of the speakers is why it changes; ambiguity has nothing to do with it. Further, desiderata in general are the product of human nature, which is what it is, whether we like it or not, and hence we always can and will have them. The inability to judge the relative merits of different systems is a cognitive defect that arises from self loathing. All that is necessary to judge relative merits is an ability to pick a metric and the minimal guts necessary to associate a value with an order on that metric. Thus I judge the English writing system to be superior to the traditional Chinese, and I am happy to do so without knowing much about Chinese. Some simple metrics to establish this judgment are the number of characters (tens of thousands vs. less than a hundred) and the relative difficulty in segmentation (lots vs. none.) This may leave some self-loathing academics aghast, but I am okay with that. Marshall === Subject: Re: Is language a mess? Am 18 Apr 2007 14:16:52 -0700 schrieb Marshall: I don't understand your second metric, can you please go into more detail on it? On the first metric: the words of classical Chinese are composed of an alphabet of eight different elements (called strokes), and only for very few words you need more than 30 of them; the average is 10 per word. English uses an alphabet of over 50 different elements, which are also more complex than the strokes; you need only five in average to write an English word. Looks comparable to me. Joachim Joachim === Subject: Re: Is language a mess? Cc: grammatim@verizon.net An interesting way to put it ... but I don't think it would appeal to anyone but a mathematician! === Subject: Re: Is language a mess? Again manifesting ignorance and bigotry. Mathematicians understand full well the hazard in identifying count with complexity. -- Michael Press === Subject: Re: Is language a mess? If you're a mathematician, you're showing that mathematicians aren't so good at understanding English. My point was that _only_ mathematicians would be interested in this particular identity of count and complexity, because the individual stroke is not the appropriate level for dissecting a Chinese character into. === Subject: Re: Is language a mess? Am 19 Apr 2007 10:21:28 -0700 schrieb Peter T. Daniels: They are probably the majority of this group. (sci.lang) Joachim === Subject: Re: Is language a mess? (was: English is a mess.) Only if you've decided that decide can refer to completely unconscious mental events. Then you're either stupid or bigoted. Where'd you get the figure tens of thousands? What is difficulty in segmentation? === Subject: Re: Is language a mess? (was: English is a mess.) Completely? No. I note that you again fail to address my objections to your claim that ambiguity is the sole driver for language change; I will consider it that you have withdrawn this claim. Yeah, I had you pegged as a self-loathing academic early on. The false dichotomy you present, that one either completely eliminates all ability to judge the value associated with any metric, or else one is completely intolerant of other opinions or ways of doing this, is quite hilarious. I'm actually chuckling as I type this. (Or I suppose in the spirit of the origin of the thread I should say I LOL'ed.) I also note you inserted your commentary *before* the point where I mention the specific metrics I used, further reinforcing the fact that you've abdicated all judgment entirely, expect for the one where you harshly judge anyone *else* who uses any judgment. Ah, the rich irony of the academic who calls people who judge things differently that he does bigoted. The point is that traditional Chinese uses many more characters than English; do you dispute it? Segmentation is the act of partitioning sequential characters into words, as distinct from parsing. It could be called tokenization, or there might be some other term for it in your discipline. Marshall === Subject: Re: Is language a mess? (was: English is a mess.) No, Marshall. Your objections are simply incoherent. Would you prefer ignorant to stupid? What you claim about Chinese writing is indeed laughable. And the assertion of your complacency in that ignorance is sheer bigotry. I inserted the commentary after the judgment. Your specific metrics have no basis in fact. Try starting with facts. define character Ok, what do you know about partitioning sequential characters into words in Chinese? What do you think parsing means in linguistics? === Subject: Re: Is language a mess? (was: English is a mess.) Then why in the world--given these claims--would you contradictorily claim that mathematics is not language? Math, demonstrably, is natural and progressive. Tom === Subject: Re: Is language a mess? [...] Which proves nothing. Observing that people look at pictorial expressions and act accordingly. Assuming that the child could ask the adult why a right turn instead of a left, or the adult tries to guide the child to recognize symbols, such as in playing with blocks with symbols on them, it can be done. Stating that it is not usually done does not mean it cannot be. [...] That early man lived in caves, or in the open, does not make building shelters unnatural. [...] Paleoliths produced by people whose spoken language is not known can often be deciphered. It would be more common if more of them were in good shape. [...] -- 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: Is language a mess? What the bloody ing hell are you referring to? suffice. === Subject: Re: Is language a mess? On 18 Apr 2007 16:43:21 -0400, Herman Rubin sci.lang,alt.philosophy,sci.math: In the mathematical sense of the word it proves nothing, but that sense is not useful in this non-mathematical context. I suggest that you think about *why* there is no such society. HOW?! By your own hypothesis the child is without language. Or haven't you realized that yet? [...] Examples? === Subject: Re: Is language a mess? It has been claimed that those who used speech killed off those, including their offspring, who did not. It does not prove the impossibility of such a society. The child who starts out babbling, and who has good hearing, is still without language. It is others who teach him that certain sound combinations have meaning. [...] I have seen such, and I have read of many more. Necessarily, they are crude, but a cave man artist can get across a fairly simple message. -- 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: Is language a mess? Jeez. Now you're talking like Condoleezza Rice (there are those who say ...). Put up or shut up. Or are you going to dispute that language didn't offer an evolutionary advantage over non-language? Does that somehow mean that the languaged killed off the unlanguaged? Are you not aware that hearing children of deaf parents have as their first language whichever signed language the parents use? Unless they are born into an extremely segregated community, they also learn as another native language the spoken language of their associates. Put up or shut up. === Subject: Re: Is language a mess? (was: English is a mess.) In what way is language natural? It is not unusual for children to make markings on walls, in sand, etc. If a child sees sufficiently simple markings made by adults, will the child not try to imitate this? -- 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: Is language a mess? (was: English is a mess.) Is that supposed to have something to do with writing? === Subject: Re: Is language a mess? Am 18 Apr 2007 18:32:08 -0700 schrieb Peter T. Daniels: Is babbling of infants supposed to have something to do with talking? Joachim === Subject: Re: Is language a mess? Don't tell me you're going to claim that scribblings gradually turn into writing during a child's development? In that case, why hasn't every language ever spoken had its own writing system? === Subject: Re: Is language a mess? How much of the following is yours, Peter, and how much is it the Five Minute Linguist ? ==Quotes from http://www.cofc.edu/linguist/archives/2005/06/where_did_writi.html [1] The discovery of writing was almost inevitable when a society grew complex enough to need it. [2] Writing turns out to be a pretty useful thing to have. And once it's discovered, nearby peoples tend to adopt it too. [3] Where would we be without writing? It's an extraordinary part of language -- and of human history. Without writing, you could reasonably ask, would history even exist? That's the linguistic thought for today, which comes to us from Peter T. Daniels, author of The World's Writing Systems. Quote [1] says that the discovery of writing is almost inevitable (dare I say natural)? I find quote [4] four particularly interesting, because it says that writing is a part of language. Clearly, orthography is a part of writing. Therefore,orthography is part of language. Didn't you say that orthography is NOT an aspect of language? === Subject: Re: Is language a mess? Am 19 Apr 2007 10:04:07 -0700 schrieb Peter T. Daniels: No, I wasn't taking Herman's position, I was just challenging the validity of your argument. Joachim === Subject: Re: Is language a mess? (was: English is a mess.) Marshall: No, but if two separate areas control the same limb in more or less the same way, then you may assume that one has grown naturally and the other was learned. That supports my point, so I think it sounds reasonable. Dunno. I gotta check the literature some day, rather than relying on second-hand sources. Well, if learning by definition can be made more efficient with the help of teaching, then no. No, but that's just because you can use learn how in the sense of begin. I wouldn't expect many parents to have thought much about it. Jens S. Larsen === Subject: Re: Is language a mess? (was: English is a mess.) I am surprised. If you don't think walking is learned then what word would you use for the acquisition of the ability to walk? I am quite certain that running can be made more efficient with the help of teaching; this is exactly what track coaches do. Would you agree that in common parlance, walking is learned? Do you have a specific technical definition of learn in mind that you could share? Marshall === Subject: Re: Is language a mess? (was: English is a mess.)