7947 Subject: Re: Racist Nonsense (snip) >> Nor are all Jewish people guilty of such behaviour. >> guilty of? luxuriate in! Really. If you shake hands and then >> can still count fingers to five, you had better check your toes. The >> culture is intensely driven by personal achievement, scholarship, and >> community approval. Centuries of enthusiastic European anti-Semitism >> plus having the bottom 90% of an already upwardly shif bell curve >> cut off during WWII resul in, well, measureable human evolution. >> It isn't a level playing field when you face a test room filled with >> folks whose average IQ is a full standard deviation higher than >> yours. You are desperately fighting for what they do as a matter of >> course. Be afraid, be very afraid. >Why? I really don't get it. Of course, I live in a household that has >a fairly high average IQ (somewhere around 145). Only 4 of the 7 are >of Jewish (very dilute) descent. One of the 7 brings down the average >(he has an IQ of 125). Strangely enough his grandfather is German. His >grandmother is one of the McCoys. Yes, those McCoys. The second lowest >has an IQ of 135. It's hard to keep the brighter kids from giving >these two a hard time at times but they usually help out their slower >siblings (step siblings in this case). >Back to your fear ... why should people be scared? The obvious thing to fear is people that believe a high IQ actually means something. :) Strangely enough, most people with high IQs are just like other people ... only those that run around trumpeting their high IQs are quite likely to be nasty pieces of work. Bruce -------------------------------------------------------------- --------- It was so much easier to blame it on Them. It was bleakly depressing to think that They were Us. If it was Them, then nothing was anyones fault. If it was Us, what did that make Me ? After all, Im one of Us. I must be. Ive certainly never thought of myself as one of Them. No-one ever thinks of themselves as one of Them. Were always one of Us. Its Them that do the bad things. <=> Terry Pratchett. Jingo. Subject: Re: Racist Nonsense > (snip) >> Nor are all Jewish people guilty of such behaviour. >> guilty of? luxuriate in! Really. If you shake hands and then >> can still count fingers to five, you had better check your toes. The >> culture is intensely driven by personal achievement, scholarship, and >> community approval. Centuries of enthusiastic European anti-Semitism >> plus having the bottom 90% of an already upwardly shif bell curve >> cut off during WWII resul in, well, measureable human evolution. >> It isn't a level playing field when you face a test room filled with >> folks whose average IQ is a full standard deviation higher than >> yours. You are desperately fighting for what they do as a matter of >> course. Be afraid, be very afraid. > >Why? I really don't get it. Of course, I live in a household that has >a fairly high average IQ (somewhere around 145). Only 4 of the 7 are >of Jewish (very dilute) descent. One of the 7 brings down the average >(he has an IQ of 125). Strangely enough his grandfather is German. His >grandmother is one of the McCoys. Yes, those McCoys. The second lowest >has an IQ of 135. It's hard to keep the brighter kids from giving >these two a hard time at times but they usually help out their slower >siblings (step siblings in this case). > >Back to your fear ... why should people be scared? > The obvious thing to fear is people that believe a high IQ actually means > something. :) Strangely enough, most people with high IQs are just like > other people ... only those that run around trumpeting their high IQs are > quite likely to be nasty pieces of work. Perhaps. We're a fairly normal family. We canoe together, 3 of the boys play soccer and go to scouts, some of the kids are interes in religion and some aren't. IQ isn't something we discuss at home. I mentioned it here because of Uncle Al's post. The kids don't know their test scores. I wasn't told mine when I was a kid either. You are right to some extent about high IQ not meaning too much. One of my sisters has a fairly high score but she was never able to learn how to do long division very well. Motivation and personality seem to be much more important in life than being more intelligent than the people who surround you. Subject: Re: Antidiagonal, Infinity About Euclid's postulates there, they define Euclidean geometry. Disagreeing with the parallel postulate, number five, allows non-Euclidean geometry. About the compass and rule to trisect an angle, for example to form an angle of pi/3 radians from lines intesecting a point on a straight line, an angle of pi radians, it's easy to bisect an angle with the compass, and 1/3 is the sum of 1 / 2^2x for each positive integer x, eg .010101(01).... A theoretical rule and compass bijection that takes infinitesimal time to bisect an angle may well trisect an angle in some finite time. When you cross the room, you get all the way there. You can begin to sample a random real number from the unit interval by flipping a coin a given number of times. What you get is a discretized sample. About y/x, say that all that is known is that y is greater than x. Is y thus a dependent variable of x? All that is known is that y > x. The value of y/x as x goes to infinity is indefinite. It might be a finite value, it might diverge. Are x and y thus interdependent? About the sets of the hyperreals and the reals, somebody else says that each set contains the same elements, that is x E R <-> x E *R. The square root of two: the length of the diagonal of the unit square, and the length of the side of the square with diagonal of length two. Two: the only integer whose sum with itself is its product with itself. Then again multiplication is just the sum of a mutiplicand with itself as many times as the other. About the itty bitty line segments, infinitesimal line segments might be comprised of a pair of adjacent points. Yet, that's not acceptible. About the representation of a continuous function as a signal, Fourier might have much to tell us about it. The real number is a point! Identify a real number. Point to it on the real number line. Where are the negative integers in the ordinals? 2 - 4 = -2. Chapman, if you're going to go outside put some pants on. I don't get that function that's continuous at all irrationals. It doesn't have an inverse, it's partial. Ross Subject: Re: Antidiagonal, Infinity <3f7cafc2$11$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310041858.3878f7c2@posting.google.com> <3f82e66f$1$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310071809.638fb9db@posting.google.com> <3f85c273$18$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310092058.2930bf11@posting.google.com> <3f89f684$43$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310131601.422ff736@posting.google.com> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith X-Treme: C&C,DWS at 05:01 PM, raf@tiki-lounge.com (Ross A. Finlayson) said: >About Euclid's postulates there, they define Euclidean geometry. Actually, they don't. >About the compass and rule to trisect an angle, for example to form >an angle of pi/3 radians The issue isn't whether there is an angle that can be trisec; the issue is whether you can trisect an arbitrary angle. >1/3 is the sum of 1 / 2^2x for each positive integer x, There is no such sum. There is a limit of sums, but you can't take a limit with compass and straighge. >A theoretical rule and compass bijection that >takes infinitesimal time A meaningless term. Mathematics is not about time. Nor is it about Zeno. >You can begin to sample a random real number You still haven't defined what you mean by a random real number. >About y/x, say that all that is known is that y is greater than x. What sorts of things are x and y? >Is y thus a dependent variable of x? What does that question mean? >The value of y/x as x goes to infinity is indefinite. What does that sentence mean? >About the sets of the hyperreals and the reals, somebody else says >that each set contains the same elements, You said that, and it's false. >Then again multiplication is just the sum of a >mutiplicand with itself as many times as the other. Pi*Pi >infinitesimal line segments Please define. >might be comprised of a pair of adjacent points. There are non. And line segments in Euclidean spaces contain more than two points. >About the representation of a continuous function as a signal, This is sci.math, not sci.ee; we don't do signals. Besides, even an EE would consider that to be nonsense. A signal is not the same thing as a sine wave. >Fourier might have much to tell us about it. Yes, he would tell you about approximating continuous functions as sums of trigonometric functions. >Point to it on the real number line. Pointing may be a valuable skill in kindergarten; it has nothing to do with Mathematics. >Where are the negative integers in the ordinals? Where are the orange groves in the Bessemer converter? There are none. >I don't get that function that's continuous at all irrationals. >It doesn't have an inverse, Why is it relevant whether it has an inverse? >it's partial. Where is it undefined? -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolici bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: Re: Antidiagonal, Infinity > About Euclid's postulates there, they define Euclidean geometry. > Disagreeing with the parallel postulate, number five, allows > non-Euclidean geometry. Actually, Euclid's axioms have been shown insufficient. > About the compass and rule to trisect an angle, for example to form an > angle of pi/3 radians from lines intesecting a point on a straight > line, an angle of pi radians, it's easy to bisect an angle with the > compass, and 1/3 is the sum of 1 / 2^2x for each positive integer x, > eg .010101(01).... A theoretical rule and compass bijection that > takes infinitesimal time to bisect an angle may well trisect an angle > in some finite time. When you cross the room, you get all the way > there. The trisection problem specifies certain rules to be followed in any attempt. Trying to do it by breaking those rules is disallowed. The remainder of Ross' post was to incoherent to comment on. Subject: Re: Antidiagonal, Infinity <3c6b9c1e.0310041858.3878f7c2@posting.google.com> <3f82e66f$1$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310071809.638fb9db@posting.google.com> <3f85c273$18$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310092058.2930bf11@posting.google.com> <3f89f684$43$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310131601.422ff736@posting.google.com> linux) >> About Euclid's postulates there, they define Euclidean geometry. >> Disagreeing with the parallel postulate, number five, allows >> non-Euclidean geometry. > Actually, Euclid's axioms have been shown insufficient. In what sense? -- Sale or rental of this disc is ILLEGAL. If you have ren or purchased this disc, please call the MPAA at 1-800-NO-COPYS. -- The MPAA begins a new anti-piracy program, found on a DVD purchased in China Subject: Re: Antidiagonal, Infinity <3f7cafc2$11$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310041858.3878f7c2@posting.google.com> <3f82e66f$1$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310071809.638fb9db@posting.google.com> <3f85c273$18$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310092058.2930bf11@posting.google.com> <3f89f684$43$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310131601.422ff736@posting.google.com> <87oewk6kn5.fsf@phiwumbda.org> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith X-Treme: C&C,DWS at 02:58 PM, jesse@phiwumbda.org () said: >In what sense? In the sense that some of the statements Euclid purpor to prove from the lis axioms and postulates don't follow from them. See, e.g., Foundations of Geometry[1] for an explanation. Google for, e.g;., Axiom of Archimedes. [1] You may see me jokingly refer to it as groundlaager, but it was a seminal book by one of the major Mathematicians of the[2] century, and still quite relevant today. [2] Whether you count him as 19th or 20th. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolici bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: Re: Antidiagonal, Infinity > >> About Euclid's postulates there, they define Euclidean geometry. >> Disagreeing with the parallel postulate, number five, allows >> non-Euclidean geometry. Actually, Euclid's axioms have been shown insufficient. > In what sense? See Hilbert's work on the subject. Subject: Re: Antidiagonal, Infinity > >> About Euclid's postulates there, they define Euclidean geometry. >> Disagreeing with the parallel postulate, number five, allows >> non-Euclidean geometry. Actually, Euclid's axioms have been shown insufficient. > In what sense? See http://www.beva.org/math323/asgn7/dec12.htm or do a Google search for Euclid and Hilbert at http://www.google.com/advanced_search?hl=en Subject: Re: Antidiagonal, Infinity <3c6b9c1e.0310041858.3878f7c2@posting.google.com> <3f82e66f$1$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310071809.638fb9db@posting.google.com> <3f85c273$18$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310092058.2930bf11@posting.google.com> <3f89f684$43$fuzhry+tra$mr2ice@news.patriot.net> <3c6b9c1e.0310131601.422ff736@posting.google.com> <87oewk6kn5.fsf@phiwumbda.org> linux) Actually, Euclid's axioms have been shown insufficient. >> In what sense? > See > http://www.beva.org/math323/asgn7/dec12.htm > or do a Google search for Euclid and Hilbert at > > http://www.google.com/advanced_search?hl=en Thanks. -- But remember, as long as one human being follows the rules of mathematics, then mathematics as a human discipline survives. Right now I'm that one human being, so mathematics survives. -- James S. Harris Subject: Re: Antidiagonal, Infinity >> Actually, Euclid's axioms have been shown insufficient. >In what sense? Presumably, in the sense that they don't model what they are (pre-mathematically) intended to model: without some sort of axiom(s) of completeness in the style of Hilbert, various points that Euclid purporly constructs just may not *be* there! (Or so I've been told.) Lee Rudolph Subject: Re: Antidiagonal, Infinity <87oewk6kn5.fsf@phiwumbda.org> linux) > Actually, Euclid's axioms have been shown insufficient. >>In what sense? > Presumably, in the sense that they don't model what they are > (pre-mathematically) intended to model: without some sort of > axiom(s) of completeness in the style of Hilbert, various > points that Euclid purporly constructs just may not *be* > there! (Or so I've been told.) I have only a passing interest, not a deep one, here, but I'd still like to have a reference. I think I understand what you're talking about, but, nonetheless, a concise and well-presen explanation would be wonderful. Thanks if you have it. A pox on you if'n you don't. -- [R]eality has a fascinating ability to check us when we get a little too big for our britches... Make no mistake. There isn't a mathematician alive today that I can't now touch, and not a mathematical career on the planet that I can't now affect. --, render of worlds Subject: Re: Antidiagonal, Infinity Actually, Euclid's axioms have been shown insufficient. >In what sense? >> Presumably, in the sense that they don't model what they are >> (pre-mathematically) intended to model: without some sort of >> axiom(s) of completeness in the style of Hilbert, various >> points that Euclid purporly constructs just may not *be* >> there! (Or so I've been told.) >I have only a passing interest, not a deep one, here, but I'd still >like to have a reference. >I think I understand what you're talking about, but, nonetheless, a >concise and well-presen explanation would be wonderful. >Thanks if you have it. A pox on you if'n you don't. I don't have a reference either, but it's a well-known fact that Euclid's axioms were not complete. ************************ Subject: Star Gate Topology of the Universe Jack, You say, In particular I do not as yet see any physical necessity for Saul-Paul's Ansatz that physical 3D expanding accelerating cosmic space is actually SU(2)/ID rather than the SU(2) shown in Fig 3... The idea that 3D cosmological space SU(2)/ID rather than SU(2) is the view of Luminet et al. in their *Nature* (9 October) paper. They say (p. 593-594): The Poincare dodecahedral space is a dodecahedral block of space with opposite faces abstractly glued together, so objects passing out of the dodecahedron across any face return from the opposite face. Light travels across the faces in the same way, so if we sit inside the dodecahedron and look outward across a face, our line of sight re-enters the dodecahedron from the opposite face. We have the ILLUSION [emphasis added] of looking into an adjacent copy of the dodecahedron. Part of the problem here is what is meant by illusion physically? On the one hand we have very pretty topological formal algorithms in which, for example, a cylinder is topologically equivalent to a flat rectangle with periodic boundary conditions on one pair of opposite edges. One can generalize this to multiply-connec 2D surfaces with wormhole handles or toroidal surfaces and take it to 3D etc. However, my point is that physically the Universe could be either, in the simplest toy model, in 2D like the curved cylinder or like the flat rectangle with a pair of Star Gate edges of the world in which material objects are instantly telepor across space. Formally, the two situations are equivalent or indistinguishable from the POV of the topology, but the local metrical physics is more than the pre-metrical global topology and the actual situation is empirical and cannot be decided apriori on purely esthetic grounds. Note that a simply-connec ruled 2D surface like the cylinder has zero intrinsic Gaussian curvature as I recall. What about the doubly-connec 2D torus? A Flatlander insect crawling on either the 2D cylinder or torus without boundary is equivalent to the insect being instantly telepor from one edge to the opposite edge across a distance c/H(t) when we make the conceptual cuts to a flat rectangle. So the issue is whether there is any physical way to distinguish the two ideas or are they absolutely degenerate or indistinguishable by any imaginable physical measurements such as the presence or absence of a local tuv(zpf) =/= 0 exotic vacuum tensor field? Now as far as the WMAP data is concerned this distinction between rubber expanding accelera versions of 1. we are literally trapped like Flatlanders inside a closed multiply connec 3D space without boundary but non-trivial Betti number with no sharply detectable 2D Star Gate walls vs 2. we are literally trapped like Flatlanders inside a 3D spherical dodecahedron with 12 pentagonal edged Star Gate walls or faces on the expanding scale c/H(t) with essentially instant teleportation to the opposite face through a traversable wormhole that is short compared to c/H(t). 2 requires the unified exotic macro-quantum vacuum dark energy/matter local zero point stress-energy density Diff(4) tensor field tuv(vac) = (c^4/8piG*)/zpfguv not to vanish at the faces in such a way as to support and maintain this huge network of traversable cosmic scale wormholes that implement the inferred global topology from the ~ 2.7 deg K CMB temperature fluctuation spherical harmonic multipole resolved statistics of WMAP. However, if we are limi only to remote-sensing of this global topology as in the WMAP space probe the above distinction is probably moot or degenerate. We will only be able to decide this perhaps by sending out warp drive space probes to see if the world has an edge or not. The local /zpf zero point dark energy/matter exotic vacuum c-number ODLRO geometrodynamic kernel of tuv(vac) also permits the implementation of globally faster-than-light Alcubierre warp drives or, equivalently, Bondi-Terletskii negative matter propulsion that is a locally self-genera weightless free float slower-than-light timelike geodesic with small curvature tidal forces inside the ship, but which appears as spacelike world line trajectory to the outside Earth bound observer using remote sensors on the craft. Since Omega(dark energy) ~ 0.666 (:-)) to 0.73 depending on which Pundit you believe, this is not such a nutty idea as it might first appear to the more faint-hear conservative reader. *Note the above kind of hypothetical warp drive technology is repor by military intelligence connec UFO investigators that IMHO pass the crackpot filter. Whether or not those reports are true is not the gedankenexperiment what is significant is that we can conceive of such a technology within mainstream physics. Kip Thorne used this method in his 1986 paper on traversable wormholes. One way to decide between 1 and 2 is to look for a time-lag in what John emphasis) but in different regions of the sky p. 567 and what Luminet et-al describe as temperature correlations in matching circles on the sky. Is there a physical distinction between a curved multiply-connec 3D space with traversable wormholes and no boundary and a flat space with Star Gate boundaries that are the 12 pentagonal faces of the spherical dodecahedron http://mathworld.wolfram.com/Dodecahedron.html ? In principle yes, since spatial curvature is a local observable and the proper distance through the alternate worm hole paths connecting opposite faces is a variable physical parameter. When the topologist has the bug or crawling insect exit on the right edge and enter on the left edge, this is pre-metrical with no concept of metric time, hence it is an incomplete physical description leaving out measurable properties of the phenomenon. Since the detailed paper on pp 593 - 595 is not available to many readers on the bcc list, let's look at some excerpts from Dodecahedral space-topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background: The current 'standard model' of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. This follows from Einstein's classical principle of equivalence combined with Heisenberg's quantum principle of uncertainty to deduce w = -1 for the equation of state for the zero point vacuum fluctuations of ANY local micro-quantum field of any spin where w = pressure/energy density. Dark energy is w = -1 exotic vacuum with a negative zero point pressure because, the effective gravitation from a region of any stuff, real or exotic vacuum, in the weak field limit obeys a Poisson equation Laplacian of the stuff ~ (G/c^2)(energy density + 3 pressure) = (G/c^2)(energy density)(1 + 3w) This universally anti-gravitates causing the expansion of 3D co-moving 3D space in the FRW metric to accelerate when the net residual micro-quantum zero point energy density from all spins is positive. The gravitating dark matter exotic vacuum has positive zero point pressure with negative zero point energy density. IMHO dark matter is not made net residual zero point energy density of the physical vacuum is its local macro-quantum coherent order parameter PSI(x,L) = |Higgs field(x,L)|e^iGoldstone phase(x,L) at scale L, coarse-grained space-time event x in the sense of a wavelet transform generalized version of the Wigner phase space density with ODLRO in the virtual electron-positron pair reduced micro-quantum density matrix. /zpf(x,L) = Lp*^-2[1 - Lp*^3|Higgs field(x,L)|^2] Lp*^2 = Lp^4/3(c/H(t))^2/3 H(now) ~ 10^28 cm Lp^2 = hG(Newton)/c^3 Lp*(now) ~ 1 fermi, i.e. 1 Gev energy scale The ordinary non-gravitating vacuum has /zpf(x,L) = 0. Einstein's gravity is from the modulation of the Goldstone phase guv(x,L) = Minkowski metric + (1/2)(Sakharov's metric elasticity tensor of Hagen Kleinert's world crystal lattice) = nuv(Minkowski) + (1/2)[du(x,L),v + dv(x,L),u] ,u is partial derivative with respect to x^u du(x,L) is the world crystal local distortion field at scale L du(x,L) = Lp*^2(Spin 1 gauge-force invariant Bohm-Aharonov Goldstone phase),u Where also [D^uDu + V(|Higgs field(x,L)|)]|Higgs field(x,L)|e^Goldstone Phase(x,L) = 0 Is the local nonlinear Diff(4)+ spin 1 gauge invariant Landau-Ginzburg equation for the macro-quantum coherent vacuum More is different local order parameter that damps down the random zero point energy density contribution to the Einstein cosmological constant / in the large-scale limit. Einstein's Riemann 4th rank tensor curvature is from disclination defect density of string topological defects of the Goldstone phase in the Kleinert world crystal lattice with unit cells of scale Lp* using the t'Hooft-Susskind world hologram conjecture. This can be generalized to include torsion fields from Suv(x,L) = (1/2)[du(x,L),v - dv(x,L),u] =/= 0 corresponding to dislocation defects in the world crystal lattice as shown by Hagen Kleinert (Free University of Berlin). Note that Lp* depends on the cosmological FRW H(t) = R(t),t/R(t). Therefore, it starts out as 10^-33 cm at the Big Bang micro -> MACRO quantum vacuum phase transition, but gets larger making the energy scale for quantum gravity lower as the universe 3D co-moving space in the FRW limit expands. This has falsifiable consequences. On the other hand, my basic theory does not require the additional world hologram conjecture of t'Hooft-Susskind Lp* = Lp^2/3L^2/3 where I take L = c/H(t) as a kind of Mach principle. Returning to the Nature paper: The WMAP data confirms the k = 0 flat space model on small scales but it is alleged that the model breaks down at large scales where Temperature correlations across the microwave sky match expectations on angular scales narrower than 60 degrees but, contrary to predictions, vanish on scales wider than 60 degrees ... The observed lack of temperature correlations on scales beyond 60 degrees means that the broadest waves are missing ... This is a bit like a cut-off in a wave guide and like the Casimir effect between two conducting plates. ... perhaps because space itself is not big enough to support them. They predict FRW Omega zero ~ 1.013 and temperature correlations in matching circles on the sky on the basis of a global topological model of a finite 3D space with no boundary that is multiply-connec with the pattern of holes, like in a more complica 3D version of a 2D torus, called Poincare dodecahedral space. These holes IMHO can be thought of as huge traversable wormholes suppor by tuv(zpf) = tuv(exotic vacuum) =/= 0 local Diff(4) tensor fields. The ordinary non-gravitating vacuum has tuv(zpf) = 0. Omega(Dark Matter) = 0.28. The claim is made that the L =2, 3, 4 multipole terms in the temperature fluctuation power spectrum (expanded in 2D spherical polar coordina harmonics of latitude and longitude over the sky) fits their dodecahedral space k = 1 model better than the k = 0 inflation flat space model -- especially for the L = 2 quadrupole where the data is calibra to fit their model exactly at L = 4. WMAP found a quadrupole only about one-seventh as strong as what would be expec in infinite flat space ... for large values of L, ranging up to L ~ 900 corresponding to small scale temperature fluctuations, the spectrum tracks the infinite universe [k = 0, Omega zero = 1]predictions exceedingly well. The CMB temperature fluctuations arise primarily (but not exclusively) from density fluctuations in the early universe. photons traveling from denser regions do a little extra work against gravity and therefore arrive cooler, while photons from less dense regions arrive warmer We need to be more careful about density here. The usual meaning is density. The repulsive dark energy phase /zpf > 0 of exotic vacuum acts like less dense because of the anti-gravity blue shift causing real far field photons from such an exotic vacuum region to arrive warmer with more energy per quantum. Just the opposite for the gravitating dark matter /zpf < 0 region of exotic vacuum. The density fluctuations across space split into a sum of three-dimensional harmonics ... just as temperature fluctuations split into a sum of two-dimensional spherical harmonics ... The low quadrupole implies a cut-off on the wavelengths of the three-dimensional harmonics. Such a cut-off presents an awkward problem in infinite flat space, because it defines a preferred length scale in an otherwise scale-invariant space. A more natural explanation invokes a finite universe ... Whereas most potential spatial topologies fail to fit the WMAP results, the Poincare dodecahedral space fits them very well. The Poincare dodecahedral space is a dodecahedral block of space with opposite faces abstractly glued together, so objects passing out of the dodecahedron across any space return from the opposite face. *This abstract topological idea seems to be, upon further reflection, absolutely physically equivalent to a closed 3D space without boundary that is multiply-connec by giant traversable wormholes or Star Gates that require tuv(exotic vacuum) to support them. The Poincare dodecahedral block of space therefore requires a network of 6 giant star gates of scale c/H(t), analogous to a 2D spherical surface with 6 wormhole handles, or a DeRham integral domain chain 3D Betti number of 6, I would imagine, for the present case. Light travels across the faces in the same way, so if we sit inside the dodecahedron and look outward across a face, our line of sight re-enters the dodecahedron from the opposite face. We have the illusion of looking into an adjacent copy of the dodecahedron. This illusion is, I suppose, physically indistinguishable from looking into the 2D face of a giant cosmic scale traversable very short Star Gate wormhole to what is on the other side. If we take the original dodecahedral block of space not as a euclidean dodecahedron (with edge angles ~ 117 degrees) but as a spherical dodecahedron (with edge angles exactly 120 degrees), then adjacent images of the dodecahedron fit together snugly to tile the hypersphere (Fig 3b), analogously to the way adjacent images of spherical pentagons (with perfect 120 degree angles) fit snugly to tile an ordinary sphere (Fig 3a). p. 594 OK my question here is whether or not there is any physics to this new formal construction such as 120 parallel finite universes next door that we can never access, or maybe we can? This led to the issue what is physical space? Is it SU(2)/ID? Note that: 12 spherical pentagons tile the surface of an ordinary sphere. They fit together snugly because their corner angles are exactly 120 degrees. Note that each spherical pentagon is just a pentagonal piece of a sphere. Note also that we cannot identify opposite edges of a 5-sided 2D pentagon to make a multiply-connec 2D surface. The 3D dodecahedron has an even number of 2D faces 12 allowing 6 traversable wormhole handles of opposite faces. Each face is a 2D star gate portal. Note also that a 2D sphere has no boundary, but that its 12 spherical pentagonal pieces do have boundaries. 120 spherical dodecahedra tile the surface of a hypersphere. The hypersphere is simply-connec with no boundary and no holes. Therefore you only have to slice it once to get it to split into two disjoint pieces. This is unlike the single 3D spherical dodecahedron that is 6-fold multiply-connec also without boundary. You have to slice it seven times to get it to split into 2 disjoint 3D pieces. Note that a 2D torus has only one hole and you have to slice it twice to make it break apart into two disjoint pieces. The problem here now is whether or not there is any physical measurable consequence of the number 120 here? Does the simply-connec 3D hypersphere with no boundary play a physical role or is it simply an esthetic formal nicety? This is one of the key questions that motiva this original thread. to be continued Poincare dodecahedral space as they describe it is exactly the same as SU(2)/ID. These authors are quite aware of this equivalence as they show in the paper Cosmic microwave background constraints on multi-connec spherical spaces, which you can download from: http://xxx.lanl.gov/abs/astro-ph/0303580 On page 2 (of this 5 page paper), they say: The finite subgroups of S^3 are the cyclic groups Zn, the binary dihedral groups D*m, the binary tetrahedral, octahedral and icosahedral groups, respectively of order n, 4m, 24, 48 and 120. Now since you are looking for a physically significant difference between SU(2)/ID and SU(2) tiled with 120 spherical dodecahedra, I should point out the fundamental significance of the volume of the 3D space, which affects both the light travel times as well as the density of the space. As these authors say: In all cases the volume of the space S^3/G is the volume of the 3-sphere S^3 divided by the order |G| of the holonomy group. structures S^3/G, and that has to do with the A-D-E classification of these spaces. This is because A-D-E Coxeter graphs classify at least 20 physically relevant mathematical objects. As I have mentioned previously, these include Coxeter (relfection) groups, Lie algebras, gravitational instanton spaces, catastrophe bundles, 2D conformal field theories, Heisenberg algebras, and much more. I have star writing this up in a Word file, and will send it to you as soon as I finish it. Saul-Paul Subject: Simple curve question... If I have the following three data sets: A B -------------- 1500 300 4000 500 6000 300 What is the best way to calculate the corresponding B for any given A? I cannot assume any specific curve shape, meaning B could be 300 100 500, but A will always be increasing. B (BTW: this is -not- homework, it is rela to mass spec analysis and my math sucks) Subject: Re: Simple curve question... Well, I would try as below: 1) assume that B reach its maximum, say M (>500), at A=3750 (mid-point of 1500-6000), 2) fit a parabolic curve open downwards to these data. Michael Leung BCC .b9.a6.b9g.97.a6l.97sD :u2Hib.6$AX1.1990766@newssvr21.news.prodigy.com... > If I have the following three data sets: > A B > -------------- > 1500 300 > 4000 500 > 6000 300 > What is the best way to calculate the corresponding B for any given A? I > cannot assume any specific curve shape, meaning B could be 300 100 500, but > A will always be increasing. > > B > (BTW: this is -not- homework, it is rela to mass spec analysis and my > math sucks) Subject: Re: Simple curve question... > BCC .b9.a6.b9g.97.a6l.97sD > :u2Hib.6$AX1.1990766@newssvr21.news.prodigy.com... If I have the following three data sets: > A B > -------------- > 1500 300 > 4000 500 > 6000 300 What is the best way to calculate the corresponding B for any given A? I > cannot assume any specific curve shape, meaning B could be 300 100 500, > but > A will always be increasing. > B (BTW: this is -not- homework, it is rela to mass spec analysis and my > math sucks) > Well, I would try as below: > 1) assume that B reach its maximum, say M (>500), > at A=3750 (mid-point of 1500-6000), > 2) fit a parabolic curve open downwards to these data. Fitting not needed. Three points specifies a unique interpolating parabola (see Lagrange or Newton interpolation). The Lagrange quadratic for these points is: y = 300*(x-4000)(x-6000)/(1500-4000)(1500-6000) + 500*(x-1500)(x-6000)/(4000-1500)(4000-6000) + 300*(x-1500)(x-4000)/(6000-1500)(6000-4000) = (x-4000)(x-6000)/37500 - (x-1500)(x-6000)/10000 + (x-1500)(x-4000)/30000 This parabola does reach a peak of 502.5 at x=3750. However, it's terribly dangerous to draw any conclusions from such a model if all you know are three points, especially if you're planning on extrapolating the model outside the range 1500-6000. Any additional info you can incorporate (such as knowledge of the location of the peak) would be helpful. - Randy Subject: Re: (matrix analysis) Is this true: A*X*B=X => A=I and B=I? >What else results about A and B can I obtain from A*X*B=X? >(this is not a HW problem!) Is X some particular matrix, or is the equation A X B=X supposed to be true for all matrices X of a certain size? Suppose A = (a_{ij}) is an m x m matrix, B = (b_{ij}) is n x n, and A X B = X for all m x n matrices X. Then taking X = e_{kl} (the matrix with 1 in position (k,l) and 0 elsewhere) we get a_{ik} b_{lj} = 1 for i=k, j=l and 0 otherwise, which implies A = cI and B = c^(-1)I for some c <> 0. 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: (matrix analysis) Is this true: A*X*B=X => A=I and B=I? >What else results about A and B can I obtain from A*X*B=X? >(this is not a HW problem!) > Is X some particular matrix, or is the equation A X B=X supposed to be > true for all matrices X of a certain size? > Suppose A = (a_{ij}) is an m x m matrix, B = (b_{ij}) is n x n, and > A X B = X for all m x n matrices X. Then taking X = e_{kl} (the matrix > with 1 in position (k,l) and 0 elsewhere) we get a_{ik} b_{lj} = 1 for > i=k, j=l and 0 otherwise, which implies A = cI and B = c^(-1)I for some > c <> 0. Dear Robert, Thank you for your answer. I remember I've got a bunch of answers from you. I really appreciate your help! For this problem, the specification is that A, B, X are all square with size of NxN... The condition that X=A*X*B is imposed to all inputs X. Basically, this is a linear 2-D separable transform, Y=A*X*B, but now I want the output to be the input, X=A*X*B. Under this condition, what should be A, and what should be B, or they have other hidden relations? complete, there are no other A and B that can satisfy the requirement... am I right? Thanks a lot, -Walala Subject: Re: (matrix analysis) Is this true: A*X*B=X => A=I and B=I? >For this problem, the specification is that A, B, X are all square with size >of NxN... The condition that X=A*X*B is imposed to all inputs X. >complete, there are no other A and B that can satisfy the requirement... am >I right? Yes, that's what I said. 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: how about A1*X*B1+A2*X*B2=X? >For this problem, the specification is that A, B, X are all square with size >of NxN... The condition that X=A*X*B is imposed to all inputs X. >complete, there are no other A and B that can satisfy the requirement... am >I right? > Yes, that's what I said. Dear Robert, Can you say something about A1*X*B1+A2*X*B2=X? Basically, I want to approximate the input X with a bunch of transforms of the input X, try to find optimal approximation in the MSE sense.... For the above problem, can I say it equals to (A1+A2)*X*(B1+B2)=X... and then A1+A2=cI, B1+B2 = c^(-1)I... Is this true? Or what else relation you can say about A1, A2, B1, B2? Thanks a lot, -Walala Subject: Re: Slow Factoring Method The method I described works in any base. It doesn't appear to be any more efficient in base 10. 1023 base 10 1023 mod 10 = 3 1*3 = 3 7*9 = 63 1023 mod 100 = 23 01*23 = 23 11*93 = 1023 *** 21*63 = 1323 31*33 = 1023 *** 41*03 = 123 51*73 = 3723 61*43 = 2623 71*13 = 923 81*83 = 6723 91*53 = 4823 07*89 = 623 17*19 = 323 27*49 = 423 37*79 = 2823 47*09 = 423 57*39 = 2223 67*69 = 4623 77*99 = 7623 87*29 = 2523 97*59 = 5723 Russell - 2 many 2 count Subject: stable marriage problem (matching) with constraints Suppose we have B boys, G girls. B=G. The boys b1 and b3 are neighbors of b2, b2 and b4 are neighbors of b3, etc. Same for the girls: g1 and g3 are neighbors of g2, g2 and g4 are neighbors of g3, etc. We want to find a matching such that it is stable, AND if the boy m(i) is matched to the girl g(j), then the neighbors of m(i) (that is, m(i-1) and m(i+1) ) must match to the neighbors of g(j) (that is, g(j-1) or g(j+1) ). Anyone can think of a good algo? Thanks! Subject: Re: stable marriage problem (matching) with constraints Sorry, my problem was ill defined, please ignore it. > Suppose we have B boys, G girls. B=G. > The boys b1 and b3 are neighbors of b2, b2 and b4 are neighbors of b3, > etc. > Same for the girls: g1 and g3 are neighbors of g2, g2 and g4 are > neighbors of g3, etc. > We want to find a matching such that it is stable, AND if the boy m(i) > is matched to the girl g(j), > then the neighbors of m(i) (that is, m(i-1) and m(i+1) ) must match to > the neighbors of g(j) (that is, g(j-1) or g(j+1) ). > Anyone can think of a good algo? > Thanks! Subject: Re: Q wrt a number-theoretic generating function > I'm reading some introductory material about Dirichlet's generating > functions of arithmetical functions, but could not find anything about > the obvious generating function > Sum_p p^{-x}, > where the sum is extended over all primes. Has it been studied? Is it > an independent function or can it be expressed in terms Riemann's > zeta? Anything else interesting about it? References? > Michele By the way, I might as well add this: exp(sum{p=primes} 1/p^x) = sum{k=1 to oo} A(k)/k^x, where A(k) = product{p=primes} 1/(a(p,k))! , and where each a(p,k) is a nonnegative integer such that p^a(p,k) is the highest power of the prime p which divides k. (I think...) Leroy Quet Subject: Re: FUNctions/Continued-Fraction Puzzle UGGG! I used the wrong word (twice). Reposting with 2 solutions replaced with proofs. Sorry. --- > But, anyway, my solution is below the replied-to message. > (This might be actually trivial. But it does not seem to be with the > little thought I have given it. In any case, perhaps I should not have > cross-pos this to rec.puzzles {if I should have even pos it to > sci.math}; but what the...) > For all real x > 1, and for some function of x, y(x); > where each y is a real, y =y(x), based on x: it is so that: f([x; x^2, x^3, x^4,...,x^m]) = [y; y^2, y^3, y^4,...,y^m], for EVERY positive integer m; where: [x; x^2, x^3, x^4,...,x^m] is the continued-fraction 1 > x + ------------------ ; > 1 > x^2 + -------------- > 1 > x^3 + --------- > .... > + 1/x^m and [y; y^2, y^3, y^4,...,y^m] is also a continued-fraction (obviously); and [x; x^2, x^3, x^4,...,x^m] converges to X; and f(w) is a real -> real function, such that f'(X) exists and is finite nonzero. > > So, what are the possible f(w)'s, given all of the conditions above?? > First, by the way, f'(X) is the (1st) derivative of f(w) at w = X, in > case this is not obvious. > I should mention that f can equate to an infinite number of functions > if it need not be analytic. If it need by analytic, however, there are > a finite number of possible functions that can equal f(w). > (So, find the set of analytic f(w)'s.) > This puzzle seems to be more difficult than I first assumed. > I will wait until Friday, at least, to post the answer if no one else > posts the solution before that. > > .... > ...the solution: > I get that the only possible analytic f is: > f(w) = w. > Proof: > limit{m -> oo} (x/y)^(2m-1) = 1. > So, x must = y. And, consequently, f(w) must = w. > * earlier result at: http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off& threadm=b4be2fdf .0110011329.389d37c%40posting.google.com&rnum=4&prev= I highly suspect my PROOF is far from the simplest. Is there a PROOF which is any simpler, even trivial? (Perhaps my result itself, that f(w) = w is the ONLY analytic function, is wrong.) Leroy Quet Subject: Re: FUNctions/Continued-Fraction Puzzle > But, anyway, my solution is below the replied-to message. > (This might be actually trivial. But it does not seem to be with the > little thought I have given it. In any case, perhaps I should not have > cross-pos this to rec.puzzles {if I should have even pos it to > sci.math}; but what the...) > For all real x > 1, and for some function of x, y(x); > where each y is a real, y =y(x), based on x: it is so that: f([x; x^2, x^3, x^4,...,x^m]) = [y; y^2, y^3, y^4,...,y^m], for EVERY positive integer m; where: [x; x^2, x^3, x^4,...,x^m] is the continued-fraction 1 > x + ------------------ ; > 1 > x^2 + -------------- > 1 > x^3 + --------- > .... > + 1/x^m and [y; y^2, y^3, y^4,...,y^m] is also a continued-fraction (obviously); and [x; x^2, x^3, x^4,...,x^m] converges to X; and f(w) is a real -> real function, such that f'(X) exists and is finite nonzero. > > So, what are the possible f(w)'s, given all of the conditions above?? > First, by the way, f'(X) is the (1st) derivative of f(w) at w = X, in > case this is not obvious. > I should mention that f can equate to an infinite number of functions > if it need not be analytic. If it need by analytic, however, there are > a finite number of possible functions that can equal f(w). > (So, find the set of analytic f(w)'s.) > This puzzle seems to be more difficult than I first assumed. > I will wait until Friday, at least, to post the answer if no one else > posts the solution before that. > > .... > ...the solution: > I get that the only possible analytic f is: > f(w) = w. > Proof: > limit{m -> oo} (x/y)^(2m-1) = 1. > So, x must = y. And, consequently, f(w) must = w. > * earlier result at: > http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off& threadm=b4be2fdf. 0110011329.389d37c%40posting.google.com&rnum=4&prev= I highly suspect my solution is far from the simplest. Is there a solution which is any simpler, even trivial? (Perhaps my result itself, that f(w) = w is the ONLY analytic function, is wrong.) Leroy Quet Subject: Re: Euler books Injector-Info: news.mailgate.org; posting-host=adsl-66-126-133-169.dsl.frsn01.pacbell.net; posting-account=48257; posting-date=1066086898 X-URL: http://mygate.mailgate.org/mynews/sci/sci.math/ 116826093ac45662ebcf7226837973 2c.48257%40mygate.mailgate.org > where can I find english or german translations of some of euler's > works in the internet? > I can't afford to buy those. I know for instance that Euler's opera > omnia is very expensive. This would be a _really_ good place to start: http://math.dartmouth.edu/~euler/welcome.html This Google search will help you find others: http://www.google.com/search?q=opera.omnia+euler HTH xanthian. -- Pos via Mailgate.ORG Server - http://www.Mailgate.ORG Subject: Re: Euler books > where can I find english or german translations of some of euler's > works in the internet? Oh, Internet. Try the Gutenberg Project, which has online full text of many classic books. One problem with many English translations of Euler is that they are so recent (published by Springer Verlag, in some cases I know) that they are still under copyright for the English text. The original Latin text of Euler's works is, of course, long since in the public domain. Hope this helps! -- Karl M. Bunday Christ has set us free. Galatians 5:1 Learn in Freedom (TM) http://learninfreedom.org/ kmbunday AT earthlink DOT net (preferred email address) Subject: Re: Euler books > they are still under copyright for the English text. The original Latin text > of Euler's works is, of course, long since in the public domain. Euler was among the last scholars to write his papers in Latin. During the 19-th century and later most papers were published in national languages. Bob Kolker Subject: Re: Michelle Lynn Marud - September 30th 1980 X-No-Archive: yes >M A R U D >13 1 18 21 4 = 57 > Michelle provided the stats today at A Buck or Two on 2nd Ave. >South. She was the 3rd of 17 people to provide stats today, she is the >Michelle has a twin sister and a little brother. << The following (courtesy of Waxy.org) is sort of an unofficial FAQ explaining the psychotic nonsense pos to Usenet by Shawn Daryl Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and me. WARNING: Read below before even thinking about responding to this twit. http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643 Usenet has the tendency to provide a public forum for those who would normally be scribbling in a closet. For example, take Daryl Shawn Kabatoff. For the last few yeahe's methodically gathered statistics from various sources, ranging from local newspaper obituary pages to the food court of the Saskatoon Midtown Plaza mall. With all the raw data he's collec, he's attempting to prove daily that our full names are in mathematical harmony with our birthdays. His rants normally focus on a single individual he's met or read about, starting with calculations rela to their birthdate and full names, blending in whatever other personal information about their family membespouses, birthplace, and career he's been able to zealotry, and personal torment. I've never seen anything like it. With all the prime numbeFibonacci sequences and biblical references, it's like reading the notebooks of Maximillian Cohen and John Nash combined. Unsurprisingly, several posts unfold to reveal a history of painful mental illness. If you have some time, take a look. I've detailed his posting history and a several sample posts below. Usenet Posting History: January 27, 1999 to July 5, 2000 as Catsco@home.com December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original posts have been removed from Google Groups archive) April 26, 2002 to Present as dar_kabatoff@hotmail.com Selec Posts: Tessa Lynne Smith Dastageer Sakhizai and Helen Smith Brett David Maki Andrew Meredith Cotton Kathryn Lee Hipperson Amanda Dawn Newton Mona Marie Etcheverry Tony Peter Nuspl Lisa Charlene McMillan Grant Allyn Wood Comments scarier still is that saskatoon is my hometown, though not my current residence. and every single place he's mentioned in his posts (most notably nervous harold's and the roastary) were either places i've been (as it's a small city of 200K) or hangouts, ie. the two places mentioned. chances are i could email some friends back home and find out if they know of him, they (my friends that is) being of the broadway-centred slacker ilk. myself, too, until i got out of there. eh, anyways. thought it odd to see all this. midtown mall. i ate my meals there, whilst waiting several days in line for star wars episode one, at the theatre across the street. pos by andy raad on May 22, 2002 06:20 PM Fascinating. It's like he's trying to take chaos and bind it into whatever rules he can find, religious, logical and otherwise. Numbers and math have a reliable pattern, something that can always be proven to true or false. People and religion do not. It reminds me of Darren Aronofsky's movie Pi. It's the story of an paraniod genius who is trying to find a pattern in Pi. A group that takes interest in his work is convinced that the existence of Pi, a number whose existence can be proven but no quantified, is proof of the existence of God. Kabatoff's hunt for patterns in something as random as name selection is a way to reconcile his deeply logical thought process with his conflicting religious views. Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday, asking him if he'd be willing to create a numerological analysis for me. I also asked him if he had seen either Pi or A Beautiful Mind, and what he thought of them. If he replies, I'll be sure to post it. I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed pumpkin pie all over my breasts for him, and my breasts turned orange. I am a pumpkin for Shawn. pos by Trisha Blondie on July 24, 2002 10:41 PM Um, that's swell. So, you're in love with him? Shawn once went to a funeral for a Jehovah Witness that shot himself and the lemon tarts were very bad, they were not only sour but were rubbery as well. Shawn said that the guy was some kind of Jehovah Witness prophet, he saw in advance that the lemon tarts at his funeral were to be very very bad, and so he shot himself. Shawn said that he never ate pumpkin pie at a funeral but would like to some day. Shawn likes pumpkin pie and so I have been practicing to make very good pumpkin pies. pos by Trisha Blondie on July 25, 2002 02:49 PM Shawn said that the lemon tarts were sour, bitter and rubbery. I don't think this guy takes notes. I think he has Total Recall, and it has driven him insane... Oh... I almost forgot... I didnt spend thousands of dollars a day tormenting Daryl... We got a deal on tormenting that fiscal year, it only came to about 37cents a day.... Mr. Kabatoff attempts to portray himself as a victim, but in fact he is a violent predatory pedoe who is well known to his local law enforcement. In his post to multiple newsgroups with the subject Collecting Mail For The Coming Anti-Christ, he encourages mothers to send him photos of their naked daughters. Mr Kabatoff explains, I personally did not want photographs being mailed to (the coming Ant-Christ) that were of underage children unless the parent was signing consent. He is banned from virtually all the shopping malls in his community because he stalks young people and sexually harasses them. He has an extensive arrest record which includes sexual molestation charges. He's been hospitalized in mental institutions about his contact with young girls in many posts. Search newsgroup archives for posts by him containing the word nubile. As part of his harrassment, he provides personal details in a public forum, such as the real names of real children, in these and other posts. About one wan her and her sister dead. http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+dead+or +in+my+bed&hl= en&lr=&ie=UTF-8&selm=asqm35%24tjq5j%241%40ID-136124. news.dfncis.de&rnu He not only curses children and prays for their death in his posts, he also enjoys attending the funerals of young people: And so, since nubile sweeties are found in greatest abundance at the funerals of high school students, then it is the funerals of high school students that make the very very best funerals, especially if there is food... I stuff my face (and my pockets) with all the good food and look at all the pretty nubile sweeties and have the time of my life.. .http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+nubile +sex&hl=en&l r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039% 40twister.socal.rr. com&rnum=1 Many of his posts are sent to alt.teens.advice. However, he liberally spams, floods and crossposts his off-topic threatening and offensive missives to countless newsgroups. Some people HAVE problems and some folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When he sends these posts to any newgroup, please help by reporting him to his ISP. Thanks. I knew of him when I was attending the University of Saskatchewan. He'd hang out in the Arts computer lab and all you'd see is screens of numbers racing by on his laptop. I have an original copy of his Collecting Mail for the Coming Anti-Christ pamphlet, and have seen him be hauled away by campus security on more than one occasion. My friends and I refer to him as Crazy Number Man. I've been posting to (and about) Shawn for over two years with big gaps in between. He has seen Pi and didn't like it and didn't think it resembled him at all. (Wrong, it fits him to a tee) He doesn't have total recall and has sta that he travels with a lap top to notate items. Also, he uses cut n' paste a lot if you read all the way through his ramblings. He is anti-social as shown by his angry statements towards those who, by his own admission, have been kind (but not kind enough) to him. Still, he's intelligent and seems to be able to take a joke on occassion. That's where I came in. ALOHA Reply to group (Unsolici e-mail is dele from the server unread if it comes from anyone not already in my addressbook. I'll never even see it) Subject: Re: Michelle Lynn Marud - September 30th 1980 Thomas (not his real name) also posts under the name of Nospam and also Maui Cop. He pos libel against me using the name of Nospam in the WaxyOrg web site and then quotes the material using the name Thomas, quoting your libel and attributing it to someone else is just more libel. And do note that Callie is not a child but is instead a woman. I have never been hospitalized in mental institutions for accosting women, but only for daring to criticize Protestant and Catholic churches. -Daryl S. Kabatoff > >M A R U D >13 1 18 21 4 = 57 Michelle provided the stats today at A Buck or Two on 2nd Ave. >South. She was the 3rd of 17 people to provide stats today, she is the >Michelle has a twin sister and a little brother. > << explaining the psychotic nonsense pos to Usenet by Shawn Daryl > Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and > me. > WARNING: Read below before even thinking about responding to this > twit. > http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643 > Usenet has the tendency to provide a public forum for those who would > normally be scribbling in a closet. For example, take Daryl Shawn > Kabatoff. For the last few yeahe's methodically gathered > statistics from various sources, ranging from local newspaper > obituary pages to the food court of the Saskatoon Midtown Plaza mall. > With all the raw data he's collec, he's attempting to prove daily > that our full names are in mathematical harmony with our birthdays. > His rants normally focus on a single individual he's met or read > about, starting with calculations rela to their birthdate and full > names, blending in whatever other personal information about their > family membespouses, birthplace, and career he's been able to > zealotry, and personal torment. I've never seen anything like it. > With all the prime numbeFibonacci sequences and biblical > references, it's like reading the notebooks of Maximillian Cohen and > John Nash combined. Unsurprisingly, several posts unfold to reveal a > history of painful mental illness. If you have some time, take a look. > I've detailed his posting history and a several sample posts below. > Usenet Posting History: > January 27, 1999 to July 5, 2000 as Catsco@home.com > December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca > Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca > January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original > posts have been > removed from Google Groups archive) > April 26, 2002 to Present as dar_kabatoff@hotmail.com > Selec Posts: > Tessa Lynne Smith > Dastageer Sakhizai and Helen Smith > Brett David Maki > Andrew Meredith Cotton > Kathryn Lee Hipperson > Amanda Dawn Newton > Mona Marie Etcheverry > Tony Peter Nuspl > Lisa Charlene McMillan > Grant Allyn Wood > Comments > scarier still is that saskatoon is my hometown, though not my current > residence. and every single place he's mentioned in his posts (most > notably nervous harold's and the roastary) were either places i've > been (as it's a small city of 200K) or hangouts, ie. the two places > mentioned. chances are i could email some friends back home and find > out if they know of him, they (my friends that is) being of the > broadway-centred slacker ilk. myself, too, until i got out of there. > eh, anyways. thought it odd to see all this. midtown mall. i ate my > meals there, whilst waiting several days in line for star wars episode > one, at the theatre across the street. > pos by andy raad on May 22, 2002 06:20 PM > Fascinating. It's like he's trying to take chaos and bind it into > whatever rules he can find, religious, logical and otherwise. Numbers > and math have a reliable pattern, something that can always be proven > to true or false. People and religion do not. It reminds me of Darren > Aronofsky's movie Pi. It's the story of an paraniod genius who is > trying to find a pattern in Pi. A group that takes interest in his > work is convinced that the existence of Pi, a number whose existence > can be proven but no quantified, is proof of the existence of God. > Kabatoff's hunt for patterns in something as random as name selection > is a way to reconcile his deeply logical thought process with his > conflicting religious views. > Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday, > asking him if he'd be willing to create a numerological analysis for > me. I also asked him if he had seen either Pi or A Beautiful Mind, and > what he thought of them. If he replies, I'll be sure to post it. > I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed > pumpkin pie all over my breasts for him, and my breasts turned orange. > I am a pumpkin for Shawn. > pos by Trisha Blondie on July 24, 2002 10:41 PM > Um, that's swell. So, you're in love with him? > Shawn once went to a funeral for a Jehovah Witness that shot himself > and the lemon tarts were very bad, they were not only sour but were > rubbery as well. Shawn said that the guy was some kind of Jehovah > Witness prophet, he saw in advance that the lemon tarts at his funeral > were to be very very bad, and so he shot himself. Shawn said that he > never ate pumpkin pie at a funeral but would like to some day. Shawn > likes pumpkin pie and so I have been practicing to make very good > pumpkin pies. > pos by Trisha Blondie on July 25, 2002 02:49 PM > Shawn said that the lemon tarts were sour, bitter and rubbery. > I don't think this guy takes notes. I think he has Total Recall, and > it has driven him insane... > Oh... I almost forgot... I didnt spend thousands of dollars a day > tormenting Daryl... We got a deal on tormenting that fiscal year, it > only came to about 37cents a day.... > Mr. Kabatoff attempts to portray himself as a victim, but in fact he > is a violent predatory pedoe who is well known to his local law > enforcement. In his post to multiple newsgroups with the subject > Collecting Mail For The Coming Anti-Christ, he encourages mothers to > send him photos of their naked daughters. Mr Kabatoff explains, I > personally did not want photographs being mailed to (the coming > Ant-Christ) that were of underage children unless the parent was > signing consent. He is banned from virtually all the shopping malls > in his community because he stalks young people and sexually harasses > them. He has an extensive arrest record which includes sexual > molestation charges. He's been hospitalized in mental institutions > about his contact with young girls in many posts. Search newsgroup > archives for posts by him containing the word nubile. As part of his > harrassment, he provides personal details in a public forum, such as > the real names of real children, in these and other posts. About one > wan her and her sister dead. http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+dead+or +in+my+bed&hl= en&lr=&ie=UTF-8&selm=asqm35%24tjq5j%241%40ID-136124. news.dfncis.de&rnu > He not only curses children and prays for their death in his posts, he > also enjoys attending the funerals of young people: And so, since > nubile sweeties are found in greatest abundance at the funerals of > high school students, then it is the funerals of high school students > that make the very very best funerals, especially if there is food... > I stuff my face (and my pockets) with all the good food and look at > all the pretty nubile sweeties and have the time of my life.. > .http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+nubile +sex&hl=en&l > r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039% 40twister.socal.rr. > com&rnum=1 > Many of his posts are sent to alt.teens.advice. However, he liberally > spams, floods and crossposts his off-topic threatening and offensive > missives to countless newsgroups. Some people HAVE problems and some > folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When > he sends these posts to any newgroup, please help by reporting him to > his ISP. Thanks. > I knew of him when I was attending the University of Saskatchewan. > He'd hang out in the Arts computer lab and all you'd see is screens of > numbers racing by on his laptop. I have an original copy of his > Collecting Mail for the Coming Anti-Christ pamphlet, and have seen > him be hauled away by campus security on more than one occasion. My > friends and I refer to him as Crazy Number Man. > I've been posting to (and about) Shawn for over two years with big > gaps in between. He has seen Pi and didn't like it and didn't think it > resembled him at all. (Wrong, it fits him to a tee) He doesn't have > total recall and has sta that he travels with a lap top to notate > items. Also, he uses cut n' paste a lot if you read all the way > through his ramblings. He is anti-social as shown by his angry > statements towards those who, by his own admission, have been kind > (but not kind enough) to him. Still, he's intelligent and seems to be > able to take a joke on occassion. That's where I came in. > ALOHA > Reply to group > (Unsolici e-mail is dele from the server unread > if it comes from anyone not already in my addressbook. > I'll never even see it) Subject: Re: Dannielle Marie Krowchuk - January 22nd 1985 X-No-Archive: yes >K R O W C H U K >11 18 15 23 3 8 21 11 = 110 > Dannielle was the second of 17 people to provide stats on July 2nd << The following (courtesy of Waxy.org) is sort of an unofficial FAQ explaining the psychotic nonsense pos to Usenet by Shawn Daryl Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and me. WARNING: Read below before even thinking about responding to this twit. http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643 Usenet has the tendency to provide a public forum for those who would normally be scribbling in a closet. For example, take Daryl Shawn Kabatoff. For the last few yeahe's methodically gathered statistics from various sources, ranging from local newspaper obituary pages to the food court of the Saskatoon Midtown Plaza mall. With all the raw data he's collec, he's attempting to prove daily that our full names are in mathematical harmony with our birthdays. His rants normally focus on a single individual he's met or read about, starting with calculations rela to their birthdate and full names, blending in whatever other personal information about their family membespouses, birthplace, and career he's been able to zealotry, and personal torment. I've never seen anything like it. With all the prime numbeFibonacci sequences and biblical references, it's like reading the notebooks of Maximillian Cohen and John Nash combined. Unsurprisingly, several posts unfold to reveal a history of painful mental illness. If you have some time, take a look. I've detailed his posting history and a several sample posts below. Usenet Posting History: January 27, 1999 to July 5, 2000 as Catsco@home.com December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original posts have been removed from Google Groups archive) April 26, 2002 to Present as dar_kabatoff@hotmail.com Selec Posts: Tessa Lynne Smith Dastageer Sakhizai and Helen Smith Brett David Maki Andrew Meredith Cotton Kathryn Lee Hipperson Amanda Dawn Newton Mona Marie Etcheverry Tony Peter Nuspl Lisa Charlene McMillan Grant Allyn Wood Comments scarier still is that saskatoon is my hometown, though not my current residence. and every single place he's mentioned in his posts (most notably nervous harold's and the roastary) were either places i've been (as it's a small city of 200K) or hangouts, ie. the two places mentioned. chances are i could email some friends back home and find out if they know of him, they (my friends that is) being of the broadway-centred slacker ilk. myself, too, until i got out of there. eh, anyways. thought it odd to see all this. midtown mall. i ate my meals there, whilst waiting several days in line for star wars episode one, at the theatre across the street. pos by andy raad on May 22, 2002 06:20 PM Fascinating. It's like he's trying to take chaos and bind it into whatever rules he can find, religious, logical and otherwise. Numbers and math have a reliable pattern, something that can always be proven to true or false. People and religion do not. It reminds me of Darren Aronofsky's movie Pi. It's the story of an paraniod genius who is trying to find a pattern in Pi. A group that takes interest in his work is convinced that the existence of Pi, a number whose existence can be proven but no quantified, is proof of the existence of God. Kabatoff's hunt for patterns in something as random as name selection is a way to reconcile his deeply logical thought process with his conflicting religious views. Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday, asking him if he'd be willing to create a numerological analysis for me. I also asked him if he had seen either Pi or A Beautiful Mind, and what he thought of them. If he replies, I'll be sure to post it. I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed pumpkin pie all over my breasts for him, and my breasts turned orange. I am a pumpkin for Shawn. pos by Trisha Blondie on July 24, 2002 10:41 PM Um, that's swell. So, you're in love with him? Shawn once went to a funeral for a Jehovah Witness that shot himself and the lemon tarts were very bad, they were not only sour but were rubbery as well. Shawn said that the guy was some kind of Jehovah Witness prophet, he saw in advance that the lemon tarts at his funeral were to be very very bad, and so he shot himself. Shawn said that he never ate pumpkin pie at a funeral but would like to some day. Shawn likes pumpkin pie and so I have been practicing to make very good pumpkin pies. pos by Trisha Blondie on July 25, 2002 02:49 PM Shawn said that the lemon tarts were sour, bitter and rubbery. I don't think this guy takes notes. I think he has Total Recall, and it has driven him insane... Oh... I almost forgot... I didnt spend thousands of dollars a day tormenting Daryl... We got a deal on tormenting that fiscal year, it only came to about 37cents a day.... Mr. Kabatoff attempts to portray himself as a victim, but in fact he is a violent predatory pedoe who is well known to his local law enforcement. In his post to multiple newsgroups with the subject Collecting Mail For The Coming Anti-Christ, he encourages mothers to send him photos of their naked daughters. Mr Kabatoff explains, I personally did not want photographs being mailed to (the coming Ant-Christ) that were of underage children unless the parent was signing consent. He is banned from virtually all the shopping malls in his community because he stalks young people and sexually harasses them. He has an extensive arrest record which includes sexual molestation charges. He's been hospitalized in mental institutions about his contact with young girls in many posts. Search newsgroup archives for posts by him containing the word nubile. As part of his harrassment, he provides personal details in a public forum, such as the real names of real children, in these and other posts. About one wan her and her sister dead. http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+dead+or +in+my+bed&hl= en&lr=&ie=UTF-8&selm=asqm35%24tjq5j%241%40ID-136124. news.dfncis.de&rnu He not only curses children and prays for their death in his posts, he also enjoys attending the funerals of young people: And so, since nubile sweeties are found in greatest abundance at the funerals of high school students, then it is the funerals of high school students that make the very very best funerals, especially if there is food... I stuff my face (and my pockets) with all the good food and look at all the pretty nubile sweeties and have the time of my life.. .http://groups.google.com/groups?q=Daryl+Shawn+Kabatoff+nubile +sex&hl=en&l r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039% 40twister.socal.rr. com&rnum=1 Many of his posts are sent to alt.teens.advice. However, he liberally spams, floods and crossposts his off-topic threatening and offensive missives to countless newsgroups. Some people HAVE problems and some folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When he sends these posts to any newgroup, please help by reporting him to his ISP. Thanks. I knew of him when I was attending the University of Saskatchewan. He'd hang out in the Arts computer lab and all you'd see is screens of numbers racing by on his laptop. I have an original copy of his Collecting Mail for the Coming Anti-Christ pamphlet, and have seen him be hauled away by campus security on more than one occasion. My friends and I refer to him as Crazy Number Man. I've been posting to (and about) Shawn for over two years with big gaps in between. He has seen Pi and didn't like it and didn't think it resembled him at all. (Wrong, it fits him to a tee) He doesn't have total recall and has sta that he travels with a lap top to notate items. Also, he uses cut n' paste a lot if you read all the way through his ramblings. He is anti-social as shown by his angry statements towards those who, by his own admission, have been kind (but not kind enough) to him. Still, he's intelligent and seems to be able to take a joke on occassion. That's where I came in. ALOHA Reply to group (Unsolici e-mail is dele from the server unread if it comes from anyone not already in my addressbook. I'll never even see it) Subject: f(x+1) = f(x) + 1/f(x) What is the family of real -> real analytic functions f(x), such that: f(x+1) = f(x) + 1/f(x) for all real x? Leroy Quet Subject: Re: f(x+1) = f(x) + 1/f(x) >What is the family of real -> real analytic functions f(x), such that: >f(x+1) = f(x) + 1/f(x) >for all real x? There cannot be any such function on all reals. If we let g=f^2, the equation yields g(x+1) = g(x) + 2 + 1/g(x), so g(x+1) > g(x) + 2. As g is non-negative, one cannot go far in the negative direction. If we look at the equation for g and ignore its positivity, it cannot be continuous for the same reason; it must be 0 somewhere. If g starts at some x_0, the asymptotics of g are g(x) ~ 2x + C + ln(x+C/2)/2 + O(ln(x)/x), where C can be a periodic function of the fractional part of x. -- 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: f(x+1) = f(x) + 1/f(x) > What is the family of real -> real analytic functions f(x), such that: > f(x+1) = f(x) + 1/f(x) > for all real x? > It can't have any roots since then the relation is undefined. It also has to diverge to the right since lim f(x) = lim f(x+1) = lim f(x) + lim 1/f(x) ==> lim 1/f(x) = 0 ==> lim f(x) = +/-infinity where the limit is taken as x-->+infinity That's all I got right now. Have a tolerable existence. Eli -- Subject: Re: f(x+1) = f(x) + 1/f(x) >> What is the family of real -> real analytic functions f(x), such that: >> f(x+1) = f(x) + 1/f(x) >> for all real x? >> > It can't have any roots since then the relation is undefined. It also has > to diverge to the right since > lim f(x) = lim f(x+1) = lim f(x) + lim 1/f(x) > ==> lim 1/f(x) = 0 ==> lim f(x) = +/-infinity > where the limit is taken as x-->+infinity > That's all I got right now. > Have a tolerable existence. Eli > -- Both your statements are also true for all derivatives of f? .... Quaternion Subject: Re: Factorial/Exponential Identity, Infinity Besides two, there actually is another integer where ths sum of it and itself is equal to the product of it and itself: zero. A binary number that is normal to base 2 has equal probability of a given element being a zero or a one, right? That is to say, statistically any contiguous finite subsequence is expec to have equal numbers of ones and zeros. Is that the same thing as its sequence having zero-density of one half? In any even length contiguous subsequence of (01)..., half the values are one and half zero. The current state of opinion appears to be that almost all real numbers are absolutely normal, that is, normal to each integer base greater than one. Then, there are uncountably many abnormal numbers. In the unit interval, then, what if normal numbers are almost half of them, with the rational numbers with zero-density of one half rounding the proportion to exactly one half? Bizarre, no? Then again, the only normal numbers thus far contrived are not shown to appear in the wild, I hear Sierpinski designed a construction of one. Yet, there is evidence that pi, for example, is not abnormal to base ten, eg, in the first million decimal digits each digit appears around 1/10 of the time. MathPages' Is e normal?: http://www.mathpages.com/home/kmath519.htm . Many (most?) sequences with equal densities of zeros and ones are not normal to base two. They don't contain every other expec sequence, ie being normal in base four, eight, etcetera. A number normal to base two is normal to base 2^x for positive integer x. I read this quote of Euler off the Internet the other day and thought it was pretty good, Euler's rather caustic: Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word sum; this idea, if thus conceived -- namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken -- has relevance only for convergent series, and we should in general give up the idea of sum for divergent series. - L. Euler I think the sum is zero. Notice that Euler has the idea of sums of divergent series. Anyways, I got to thinking about the factorizations of ((sum n)^x - sum(n^x)) / s(n+1, n-x+1). I noticed the patterns of some of the factofor example how for five values of x in a row the possible rational function, or ratio of polynomials, if it exists, that goes to x!, has the given factor. Then again, I'm still trying to determine an efficient method to determine a type of additive partitioning of a number, for use in enumeration. As well, I'd like to read more about the consideration of hypermatrices. I star this thread because I had the notion that half the sequences had densities of one half. Yet we have seen that n!/(n/2)!^2 2^n evaluates to a different asymptotic expression than that, yet now I read that multitudinous numbers are normal. Ross Subject: Re: Factorial/Exponential Identity, Infinity > Besides two, there actually is another integer where ths sum of it and > itself is equal to the product of it and itself: zero. x*x = x + x being a quadratic equation, how many solutions did you expect to find? > The current state of opinion appears to be that almost all real > numbers are absolutely normal, that is, normal to each integer base > greater than one. Then, there are uncountably many abnormal > numbers. I do not see that your conclusion follows from your premise. > In the unit interval, then, what if normal numbers are almost half of > them, with the rational numbers with zero-density of one half rounding > the proportion to exactly one half? Since almost all and almost half are incompossible, why ask? > Bizarre, no? Your thought processes are indeed bizarre. > Then again, the only normal numbers thus far contrived are not shown > to appear in the wild, I hear Sierpinski designed a construction of > one. Yet, there is evidence that pi, for example, is not abnormal to > base ten, eg, in the first million decimal digits each digit appears > around 1/10 of the time. > MathPages' Is e normal?: http://www.mathpages.com/home/kmath519.htm > . > Many (most?) sequences with equal densities of zeros and ones are not > normal to base two. They don't contain every other expec sequence, > ie being normal in base four, eight, etcetera. A number normal to > base two is normal to base 2^x for positive integer x. > I read this quote of Euler off the Internet the other day and thought > it was pretty good, Euler's rather caustic: > Notable enough, however, are the controversies over the series 1 - 1 > + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although > others disagree. ... Understanding of this question is to be sought in > the word sum; this idea, if thus conceived -- namely, the sum of a > series is said to be that quantity to which it is brought closer as > more terms of the series are taken -- has relevance only for > convergent series, and we should in general give up the idea of sum > for divergent series. - L. Euler > I think the sum is zero. Notice that Euler has the idea of sums of > divergent series. Even Homer nods. Subject: Integer-Alteration Game Each player takes turns coming up with algorithmic steps, one step at a time in sequence, each step giving a rule to transform an integer into another. (such as: multiply m by greatest prime p, where p divides m and is <= sqrt(|m|). If no such prime exists, leave m unchanged.) (or such as: m = floor(|m|/d(|m|)), where d(m) is number of positive divisors of m.) (or rules may involve meta-transformations, such as sending players to previous rules, depending somehow upon the value of the integer when reaching the step.) Anyway, players are encouraged to be creative when inventing rules! Each step is capable of transforming any integer, always giving an integer as output. After a predetermined number of steps have been crea (the same number for each player), a random integer is genera somehow. Players then try to guess what the output intger will be. The algorithm is run using the random start-integer. The winner of the game is the player who comes closest to guessing the final output integer. (needs work....) Leroy Quet Subject: Re: absolute value graph > Scott Eliason escribi.97 en el mensaje > Sketch the graph of f(x)=2abs(x) > ------ > 1+x^2 How would I start this question? > This function is even, i.e. f(-x) = f(x). Then sketch the graph of f(x) = > 2x/(1 + x^2) for x >= 0. and reflect it on the OY axis. Not that the above is a bad answer, but here's another perspective. Near the zero of f[x] (@ x=0 obviously), the graph looks like an absolute value function - v-shaped. When x is big - in either direction, f[x] is positive and near zero - like a reciprocal function, in fact. Apparently then, for some x in between 0 and really big, your function f must have had a maximum value... hth, cdj Subject: {Field Theory} Please help me understand this special case (was This could get confusing fast...) In my other thread I poin out that in a field F of integethe notation ab of two elements of that field is ambiguous, namely because it has the 3 possible and not necessarily equal interpretations: 1. ab = a * b where * is the multiplication of F 2. ab = (a + a + ... + a) (b times) 3. ab = (b + b + ... + b) (a times) Some people were replying to the effect that the 3 are in fact equal. And they are, when F is well behaved. But since it was confusing me so much, I sought a counterexample, and lo and behold I found one with little difficulty. This, I exhibit thus: let F as a set (not a field yet) simply equal Z, ie, all integers (do not confuse with Z_n) Now let p:N->Q be the mapping of N to Q which is used in Cantor's famous proof that the rationals are countable. For example, p(1)=1, p(2)=1/2, p(3)=2, p(4)=3, p(5)=1/3, etc. Now enhance p into a better function q defined by: for x > 0, q(x) = p(x) for x = 0, q(x) = q(0) = 0 for x < 0, q(x) = -p(-x) Finally let q' be the inverse of q. (I'll leave the existence proof details to you since it is all quite easy) Now associate with F the following addition and multiplication: a + b = q'[q(a)+q(b)] a * b = q'[q(a)q(b)] It is not hard to prove that F is thus turned into a field (with 1 as its unit and 0 as its zero) What, then, can we make of 5*3? Let us check the 3 possible interpretations: 1. 5*3 = f'[f(5)*f(3)] = f'[(1/3) * 2] = f'(2/3) = 7 2. 5*3 = 5 + 5 + 5 = f'[f(5)*3] = f'[1] = 1 3. 5*3 = 3 + 3 + 3 + 3 + 3 = f'[f(3)*5] = f'[10]. I didn't bother to write out Cantor's table all the way needed to calculate f'[10] but it is obviously way larger than 7. I have thus exhibi that the notation in question is indeed ambiguous. I am greatly muddled on the matter and am seeking clarification... Some have responded that there is no such thing as a field of integers... but this seems to make no sense to me. Yes, I can see how you can argue that Z_p is really a field of sets, not of integers, although I see nothing forbiding us from using {0,1,...,p-1} as the set and simply modifying the addition and multiplication so the modular arithmetic takes place there, and thus obtain a finite field of integers. Is it the case that the definition of a field is really some arcane, ethereal thing taught in Ph.D. level math and that Herstein's definition is just a handwaving gesture similar to an algebra 101 definition of the rationals? Subject: Re: {Field Theory} Please help me understand this special case (was This could get confusing fast...) > In my other thread I poin out that in a field F of integethe One can indeed label the congruence classes of the finite field Z/(p) by integee.g. the congruence class representatives 0,1,2,...,p-1. The proper terminology here is a residue field of the ring of integers, or image field..., not field of integers. > notation ab of two elements of that field is ambiguous, namely > because it has the 3 possible and not necessarily equal > interpretations: > 1. ab = a * b where * is the multiplication of F > 2. ab = (a + a + ... + a) (b times) > 3. ab = (b + b + ... + b) (a times) > Some people were replying to the effect that the 3 are in fact equal. > And they are, when F is well behaved. But since it was confusing me Well-behaved field? That is not a mathematical term. In any case, the example I give below should help to alleviate any confusion here. > so much, I sought a counterexample, and lo and behold I found one with > little difficulty. This, I exhibit thus: > let F as a set (not a field yet) simply equal Z, ie, all integers (do > not confuse with Z_n) > Now let p:N->Q be the mapping of N to Q which is used in Cantor's > famous proof that the rationals are countable. For example, > p(1)=1, p(2)=1/2, p(3)=2, p(4)=3, p(5)=1/3, etc. > Now enhance p into a better function q defined by: > for x > 0, q(x) = p(x) > for x = 0, q(x) = q(0) = 0 > for x < 0, q(x) = -p(-x) > Finally let q' be the inverse of q. (I'll leave the existence proof > details to you since it is all quite easy) > Now associate with F the following addition and multiplication: > a + b = q'[q(a)+q(b)] > a * b = q'[q(a)q(b)] > It is not hard to prove that F is thus turned into a field (with 1 as > its unit and 0 as its zero) > What, then, can we make of 5*3? Let us check the 3 possible > interpretations: > 1. 5*3 = f'[f(5)*f(3)] = f'[(1/3) * 2] = f'(2/3) = 7 > 2. 5*3 = 5 + 5 + 5 = f'[f(5)*3] = f'[1] = 1 > 3. 5*3 = 3 + 3 + 3 + 3 + 3 = f'[f(3)*5] = f'[10]. You are somehow confused. For an enlightening example let's consider the isomorphism between the ring of Roman numerals and the ring of integers: V times III = q'(q(V) * q(III)) = q'(5*3) = q'(15) = XV V plus V plus V = q'(q(V) + q(V) + q(V)) = q'(5+5+5) = q'(15) = XV III plus...plus III = q'(q(III)+...+q(III)) = q'(3+3+3+3+3) = q'(15) = XV The roman numerals are simply new names for the integeand the operations on them may be performed by translating the numerals to their standard names, performing the standard operations, then mapping the standard result to its Roman numeral. For further discussion of such isomorphisms see my prior post http://google.com/groups?selm=y8zu1bw7c13.fsf% 40nestle.ai.mit.edu -Bill Dubuque > I didn't bother to write out Cantor's table all the way needed to > calculate f'[10] but it is obviously way larger than 7. > I have thus exhibi that the notation in question is indeed > ambiguous. I am greatly muddled on the matter and am seeking > clarification... > Some have responded that there is no such thing as a field of > integers... but this seems to make no sense to me. Yes, I can see > how you can argue that Z_p is really a field of sets, not of integers, > although I see nothing forbiding us from using {0,1,...,p-1} as the > set and simply modifying the addition and multiplication so the > modular arithmetic takes place there, and thus obtain a finite field > of integers. Is it the case that the definition of a field is really > some arcane, ethereal thing taught in Ph.D. level math and that > Herstein's definition is just a handwaving gesture similar to an > algebra 101 definition of the rationals? Subject: Re: {Field Theory} Please help me understand this special case (was This could get confusing fast...) X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith X-Treme: C&C,DWS at 07:00 PM, snizpilbor@yahoo.com (Sniz Pilbor) said: >In my other thread I poin Claimed. >field F of integers, The integers don't form a field. >and not necessarily equal interpretations: Incorrect. >Some people were replying to the effect that the 3 are in fact >equal. And they are, when F is well behaved. What do you mean by well behaved? If F is a filed then there are a well defined mappings *_1: ZxF -> F, *_2: FxZ -> F and I: Z -> F such that all three are equivalent once you make the functions explicit. >I found one Nope. It's not a counter example. You just got confused about what operator to apply when. >Now associate with F the following addition and multiplication: >a + b = q'[q(a)+q(b)] >a * b = q'[q(a)q(b)] You'll need to make everything explicit to see your error. Use distinct symbols for the operations in Z and in F. >It is not hard to prove that F is thus turned into a field (with 1 >as its unit and 0 as its zero) Only if p(1)=1. >What, then, can we make of 5*3? Nothing, without context. It might refer to any of your interpretations 1-3, all of which give the same result, or it might refer to a 4th interpretation, which gives a different result. >Some have responded that there is no such thing as a field of >integers... Let me rephrase that: it is not a standard Mathematical term, and you have not defined it. >I see nothing forbiding us from using {0,1,...,p-1} as the set or {0,1,3,4,...p}. Would that satisfy your definition of filed of integers? >simply modifying the addition and multiplication so the modular >arithmetic takes place there, If you chose different addition and multiplication operatowould you still call it a field of integers? >Is it the case that the definition of a field is really some arcane, >ethereal thing taught in Ph.D. level math No: what is the case is that when you introduce new nomenclature you are obliga to define it. Until you have a subject well and truly under you belt, introducing new nomenclature in a question is more likely to confuse the issue than to help. Introducing new nomenclature without a definition is guarantied to confuse the issue, since the readers are not likely to interpret it the same way that you do. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolici bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: Re: {Field Theory} Please help me understand this special case (was This could get confusing fast...) > In my other thread I poin out that in a field F of integethe > notation ab of two elements of that field is ambiguous, namely > because it has the 3 possible and not necessarily equal > interpretations: > 1. ab = a * b where * is the multiplication of F > 2. ab = (a + a + ... + a) (b times) > 3. ab = (b + b + ... + b) (a times) > Some people were replying to the effect that the 3 are in fact equal. > And they are, when F is well behaved. This has nothing to do with F being well beheved or not. It is a consequence of the way in which integers are defined within a ring R (with identity) in general: one uses the unique ringhomomorphism from Z to R. More generally (anticipating your example below) one can define the integers within a monoid M (= semigroup with identity) by using the unique monoid-homomorphism from N to M. > But since it was confusing me > so much, I sought a counterexample, and lo and behold I found one with > little difficulty. This, I exhibit thus: > let F as a set (not a field yet) simply equal Z, ie, all integers (do > not confuse with Z_n) > Now let p:N->Q be the mapping of N to Q which is used in Cantor's > famous proof that the rationals are countable. For example, > p(1)=1, p(2)=1/2, p(3)=2, p(4)=3, p(5)=1/3, etc. This is interesting but beside the point. Your p is not a homomorphism. Marc Subject: Re: {Field Theory} Please help me understand this special case (was This could get confusing fast...) > Some people were replying to the effect that the 3 are in fact equal. > And they are, when F is well behaved. > > This has nothing to do with F being well beheved or not. > It is a consequence of the way in which integers are defined > within a ring R (with identity) in general: one uses the unique > ringhomomorphism from Z to R. > More generally (anticipating your example below) one can define the > integers within a monoid M (= semigroup with identity) by using > the unique monoid-homomorphism from N to M. Thanks for the reply, but did you actually read the post before replying? By integers I was meaning the normal integethat is, 1, 2, 3, -1, -2, -3, 0, etc., encountered in basic high school algebra, not generalized integers of a ring. I apologize if this caused additional confusion. As for the ambiguity, in the post to which you replied I gave a specific example where the 3 interpretations of 3*5 all ended up being completely different. Your reply seems to be saying that no, no, they are all equal, whether or not F is well-behaved. Where, then, was my mistake? Was the F which I exhibi in my post not in fact a field, and if so why not, which axiom(s) of the field did it fail to uphold? The previous response to my post, whose writer seems to have actually read it through before replying, seemed to clear things up, but now the waters are rendered as muddy as ever. I sincerely want to understand what you are saying, but you must not begrudge me to remain skeptical when a counterexample is right in front of us which you have not explained. > This is interesting but beside the point. Your p is not a homomorphism. I never claimed that it was (why would it matter?). I was using it as a means of defining an addition and multiplication which would make F a field. I get the impression that you read just that far and then stopped. The original confusion of the ambiguity seems to be even greater when learned field theoreticians rise in abundance to say it doesn't exist, *blatantly ignoring the counterexample right there*. The original post in this thread (with some minor corrections): > In my other thread I poin out that in a field F of integethe > notation ab of two elements of that field is ambiguous, namely > because it has the 3 possible and not necessarily equal > interpretations: > 1. ab = a * b where * is the multiplication of F > 2. ab = (a + a + ... + a) (b times) > 3. ab = (b + b + ... + b) (a times) > Some people were replying to the effect that the 3 are in fact equal. > And they are, when F is well behaved. But since it was confusing me > so much, I sought a counterexample, and lo and behold I found one with > little difficulty. This, I exhibit thus: > let F as a set (not a field yet) simply equal Z, ie, all integers (do > not confuse with Z_n) > Now let p:N->Q+ be the mapping of N to Q+ (the positive rationals) > which is used in Cantor's > famous proof that the rationals are countable. For example, > p(1)=1, p(2)=1/2, p(3)=2, p(4)=3, p(5)=1/3, etc. > Now enhance p into a better function q defined by: > for x > 0, q(x) = p(x) > for x = 0, q(x) = q(0) = 0 > for x < 0, q(x) = -p(-x) > Finally let q' be the inverse of q. (I'll leave the existence proof > details to you since it is all quite easy) > Now associate with F the following addition and multiplication: > a + b = q'[q(a)+q(b)] > a * b = q'[q(a)q(b)] > It is not hard to prove that F is thus turned into a field (with 1 as > its unit and 0 as its zero) > What, then, can we make of 5*3? Let us check the 3 possible > interpretations: > 1. 5*3 = q'[q(5)*q(3)] = q'[(1/3) * 2] = q'(2/3) = 7 > 2. 5*3 = 5 + 5 + 5 = q'[q(5)*3] = q'[1] = 1 > 3. 5*3 = 3 + 3 + 3 + 3 + 3 = q'[q(3)*5] = q'[10]. > I didn't bother to write out Cantor's table all the way needed to > calculate q'[10] but it is obviously way larger than 7. > I have thus exhibi that the notation in question is indeed > ambiguous. I am greatly muddled on the matter and am seeking > clarification... > Some have responded that there is no such thing as a field of > integers... but this seems to make no sense to me. Yes, I can see > how you can argue that Z_p is really a field of sets, not of integers, > although I see nothing forbiding us from using {0,1,...,p-1} as the > set and simply modifying the addition and multiplication so the > modular arithmetic takes place there, and thus obtain a finite field > of integers. Is it the case that the definition of a field is really > some arcane, ethereal thing taught in Ph.D. level math and that > Herstein's definition is just a handwaving gesture similar to an > algebra 101 definition of the rationals? Subject: Re: {Field Theory} Please help me understand this special case (was This could get confusing fast...) > In my other thread I poin out that in a field F of integethe > notation ab of two elements of that field is ambiguous, namely > because it has the 3 possible and not necessarily equal > interpretations: > 1. ab = a * b where * is the multiplication of F > 2. ab = (a + a + ... + a) (b times) > 3. ab = (b + b + ... + b) (a times) > Some people were replying to the effect that the 3 are in fact equal. > And they are, when F is well behaved. But since it was confusing me > so much, I sought a counterexample, and lo and behold I found one with > little difficulty. This, I exhibit thus: > let F as a set (not a field yet) simply equal Z, ie, all integers (do > not confuse with Z_n) > Now let p:N->Q be the mapping of N to Q which is used in Cantor's > famous proof that the rationals are countable. For example, > p(1)=1, p(2)=1/2, p(3)=2, p(4)=3, p(5)=1/3, etc. > Now enhance p into a better function q defined by: > for x > 0, q(x) = p(x) > for x = 0, q(x) = q(0) = 0 > for x < 0, q(x) = -p(-x) For this to give a bijection you probably meant that p is a bijection between N and the POSITIVE rationals. > Finally let q' be the inverse of q. (I'll leave the existence proof > details to you since it is all quite easy) > Now associate with F the following addition and multiplication: > a + b = q'[q(a)+q(b)] > a * b = q'[q(a)q(b)] > It is not hard to prove that F is thus turned into a field (with 1 as > its unit and 0 as its zero) This is correct, since the addition and multiplication is now that of the rationals. We simply decided to give them funny and unnatural names via q and q'. > What, then, can we make of 5*3? Let us check the 3 possible > interpretations: > 1. 5*3 = f'[f(5)*f(3)] = f'[(1/3) * 2] = f'(2/3) = 7 > 2. 5*3 = 5 + 5 + 5 = f'[f(5)*3] = f'[1] = 1 > 3. 5*3 = 3 + 3 + 3 + 3 + 3 = f'[f(3)*5] = f'[10]. Since in your field 1+1+1 is not equal 3 nor is 1+1+1+1+1 equal to 5, the computations 2. and 3. are incorrect, unless interpre as below (when there is no reason to expect them to be equal to computation 1.). Nothing exciting about it. > I didn't bother to write out Cantor's table all the way needed to > calculate f'[10] but it is obviously way larger than 7. > I have thus exhibi that the notation in question is indeed > ambiguous. I am greatly muddled on the matter and am seeking > clarification... You seem to suffer from the following confusion: When the notation m*r, where m is an integer and r is an element of ring, is defined, it is done using ONLY the operations of the ring. Remember, only the ring addition and ring multiplication exist (at that moment). Let me add tags _R and _Z to denote that the element or operation is that of the ring R or of the integers Z. Observe that we actually have a third multiplication taking place between an element of a ring and an element of the ring, denote this by *_M (M stands for module, you will learn about these in your next algebra course). Multiplication by adding together copies of an element of the ring necessitates that there is an integer participating to the proceedings, i.e. this is the module multiplication. So, we define module multiplication as follows: 1) Start with defining multiplication by the integers 0 and 1: 0_Z *_M r_R = 0_R, 1_Z *_M r_R = r_R 2) Extend the definition (by induction) to larger positive integers so as to satisfy one of the Z-module axioms: (n_Z +_Z m_Z)*_M r_R= (n_Z *_M r_R) +_R (m_Z *_M r_R) 3) Extend the definition to negative integers by the usual trick of using the additive inverse (within the ring) Your algebra textbook then hopefully shows a list of natural looking consequencies of this definition of module multiplication, such as (n_Z *_Z m_Z) *_M r_R = n_Z *_M (m_Z *_M r_R). As a consequence of this definition we then end up with e.g. 3_Z *_M r_R = (1_Z +_Z 1_Z +_Z 1_Z)*_M r_R = (1_Z *_M r_R) +_R (1_Z *_M r_R) +_R (1_Z *_M r_R) = r_R +_R r_R +_R r_R as expec (here again the module multiplication axiom was used). Observe that of the various multiplications present: 1) *_Z applies, when both sides are integers 2) *_R applies, when both sides are ring elements 3) *_M applies, when one is integer and the other from the ring. Your example consis of the following 3 different multiplications 1. 5_R *_R 3_R 2. 5_R *_M 3_Z 3. 5_Z *_M 3_R There is no reason, why these should be the same, when *_R is very unnatural as was the case here. You muddied the waters by making ring multiplication by 3 (really by 3_R) to be different from module multiplication by 3 (really by 3_Z). Algebra textbooks often denote all of these simply by *. You are correct in that, if you cook up something really weird (such as your example), then a confusion may result. When a confusion is a possibility, it is IMHO the responsibility of the cook to clearly indicate what is meant (e.g. by adding the subscripts to the operations as above). You may feel that it is a disservice to the students not to emphasize this distinction. I DO notify my freshman algebra students of these distinctions, but I won't unduly emphasize it and stick to the standard notation in class room usage. The reason to this is that it is part of their education to: A) be aware of these distinctions, B) be able to interpret a possibly ambiguous formula correctly from the context (this is necessary for them to be able to study more algebra on their own), C) be aware of the fact that usually the distinctions don't result in any changes (which is why the same notation is used). Good luck in your studies, Jyrki Lahtonen, Turku, Finland Subject: 1/m +1/(m+1) +...+1/n close to x Let m be a fixed positive integer. Let x be a fixed positive real. Let n(m,x) be the highest positive integer such that 1/m + 1/(m+1) + 1/(m+2) + ...+ 1/n(m,x) <= x. A lot of questions can be asked about this. But what I am wondering now is, what is: E(m,x) = x - (1/m + 1/(m+1) + 1/(m+2) + ...+ 1/n(m,x)) asymptotical to? All this is highly rela to the topic at: http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off& threadm=agt133%2 Subject: Re: Two-planes in Four-Space > Let G(2,4) be the Grassmanian of 2-dimensional subspaces in R^4. > I map G(2,4) -> RP^2 as follows. Given a plane g, choose an > orthogonal basis e1, e2. Identifying R^4 with the quaternions in > the obvious way, form the quaternion u = e1 * e2^(-1). Then > u is a square root of -1, well defined up to a sign. The square > roots of -1 are naturally identified with the unit ball S^2 sitting > in R^3 sitting in R^4 via (a,b,c) |-> (0,a,b,c), so u gives a > well-defined element of S^2/(plus or minus 1) = RP^2. One might add that the fiber F_u over the point in RP^2 represen by the quaternion u has a natural group structure: Given two planes g1 and g2 in F_u, it follows that the set g1 g2 = {p q |p in g1 and q in g2} is also a plane in F_u. This fiber is naturally isomorphic to H^*/(R+Ru)^* . Another characterization of F_u is that it consists of all planes that are fixed by the 90 degree rotation represen by u. Now I repeat my two questions: 1) We now have a fibration G(2,4) -> RP^2 in which the fibers are naturally isomorphic to the various groups H^*/(R+Ru)^*, where u ranges over square roots of -1 in the quaternions. Is there a standard name for this fibration? 2) Two planes g1 and g2 are in the same fiber F_u if and only if there exists a quaternion p such that p g1 = g2 (or equivalently, if and only if there exists a 90 degree rotation that fixes both g1 and g2). Is there a standard name for this equivalence relation? Subject: Re: help me...my problem?? > sequence {An} > A1 = 1 > A2 = 8 > An = root (An-1 * An-2) (n=3,4,5....) > find lim An (n->infinite) > --------------------------------- > i want your warm advice. > help me...please =========== Subject: Re: help me...my problem?? Original Format Nice question ! Denote D=(0,infty). Suppose that f:(0,infty)--->f(D) is continuous and strictly monotonic. Let F: f(D) --->(0,infty) be its inverse function. Instead of geometric mean let us consider the ,,f-quasi mean M_f(a,b) of two positive numbers a,b, that is (*) M_f(a,b)=F((f(a)+f(b))/2) . For instance f(x)=ln(x) ===> M_f(a,b)=sqrt(ab) : =root(ab) =geometric mean f(x)=x ====> M_f(a,b)=(a+b)/2 = arithmetic mean f(x)=1/x =====> M_f(a,b)=2ab/(a+b)= harmonic mean f(x)=x^2 =====> M_f(a,b)=sqrt((a^2+b^2)/2) = quadratic mean f(x)=x^r =====> M_f(a,b)=sqrt[r]((a^r+b^r)/2)= mean of order-r , (r integer >=2). The last mean can be generalized as / ((a^r+b^r)/2)^{1/r} for real r , r=/=0 , and MEAN_r(a,b):=/ lim_{r-->0}A_r(a,b)=G(a,b):= sqrt(ab) when r=0 . Let 0=1} defined by (1) A(n)=M_f(A(n-1),A(n-2)) , n=3,4,... , with A(1)=p , A(2)= q . By summing equalities 2*Y(k)=Y(k-1)+Y(k-2) , (k=3,4,...,n) we obtain 2*SUM_{k=3 to k=n}Y(k)=SUM_{k=2 to k=n-1}Y(k) + SUM_{k=1 to k=n-2}Y(k) that is (2) 2*Y(n) + Y(n-1) = Y(1) +2*Y(2) . Because min{a,b} =< M_f(a,b) =< max{a,b} for a,b >0, it's easy to prove that (X(n))_{n>=1}, and therefore also (Y(n))_{n>=1}, are convergent. Let LIM:=lim_{n-->infty}A(n), L:= lim_{n-->infty} Y(n)= f(LIM), or LIM=F(L) . and thus L = lim_{n-->infty}Y(n)=(Y(1)+2*Y(2))/3 . In conclusion ================================================== LIM:= lim_{n--->infty}A(n)=F((Y(1)+2*Y(2))/3)= F( (f(A(1)+2*f(A(2))/3) . ================================================== For instance , when r is a real number f(x)=x^r (when r=/=0) , and f(x)= ln(x) when r=0 , we find for (A(n))_{n>=1} genera by A(1)=p , A(2)=q , 0infty} A(n)= Sqrt[3](64) =4 . ======== Note: Let D=(0,infty), f:D--->f(D)) be a continuous strictly monotonic function and F: f(D)-->D its inverse function. An interesting question may be : Suppose as fixed the following numbers : k = a positive integer , k>=2 , p_1,p_2,...,p_k , (p_j >0 , j=1,2,...,k) , w_1,w_2,...,w_k are positiv numbers such that w_1+w_2+...+w_k = 1 . Furher let ============================================================== ========== A_f(a_1,a_2,...,a_k):=F(w_1*f(a_1)+w_2*f(a_2)+...+w_k*f(a_k)) , a_j > 0 . ============================================================== ========== Define the sequence (S(n))_{n>=1} by S(1)=p_1 , S(2)=p_2 ,...,S(k)=p_k , and S(n)= A_f(S(n-1),S(n-2),S(n-3),...,S(n-k)) , n in {k+1,k+2,...} . =========== NEW QUESTION: what about the convergence of sequence (S(n))_{n>=1} ? ======== Subject: Re: JSH: About time > Now that I've revealed the odd and you could say esoteric error in core mathematics with such a short, and rather simple argument, the > issue now is how long until mathematicians decide that they'd rather > have correct mathematics versus the *belief* that they had been > perfect in keeping error out of the collec body of work that is > called mathematics. > Really, I can not understand your work, not even the core error problem. > I apologize for replying in a public forum, but I've chosen, or been > guided, to work under certain constraints. The danger of e-mail is the > temptation to say different things to different people. It would be > better for me, professionally, to hide my support for you, but I refuse > to do it. Don't worry about it, as I find I'm liking your posts. Actually, I kind of got a kick out of some of your previous posts back when you were insulting me. My thinking is that you appreciate quality work when you see it. Now for those who wonder, being rather pissed at my current predicament, with *some* mathematicians--I have to remember not to characterize all of them--lying about my work or running away from it, I sent Jim Ferry and a testy email, where I informed them I considered them to be runners as well, and I would chase them down with the rest, by getting a computerized proof check of my work. And I also told Ferry to look for a job outside of mathematics. Now, I'm not so angry, and I think that maybe I shouldn't have sent that email, but then again, it all revolves around the question of whether or not Jim Ferry does understand the math. > My work is out there and rather easy to go over as can be seen at the > Hong Konk math site: > See http://mathdb.math.cuhk.edu.hk/forum/e_show.php?msg=782 > And I send people there because their allowal of the use of LaTeX > makes for a *much* better presentation, and given the *social* issues > I'm facing, I need all the help I can get. > The social issues. Indeed. What help could I be to you with the > mathematical issues? Even herd mathematicians like Magidin are better > at math than I. The fact is, you don't *need* any help with the > mathematical issues. Ah yes, rather prescient of you to emphasize need. It seems to me that things are about to get interesting. > I'm still working on your Plan. I've very busy right now, but I'm > finding ways to make the time for it. It will take several weeks > at least. As I began to conceive/receive it, I realized that it > would do no good if you had a Bush-like outlook on life. You seemed > annoyed by my detour into politics, but this is what I mean: you > being concerned with *mathematical* issues is like Bush trying to > build bigger bombs to fight terrorism. America is already powerful > enough, and doesn't need to become all-mighty so that all nations of > the world cower at the thought of incurring its wrath. According to > Bush, terrorists and the people who cheer for them are insane and evil. > According to Bush, a vast segment of the Islamic world is insane and evil. Bush is having issues with his father, so he reversed his father on everything. Bush Sr. said he wouldn't raise taxes and did. So Bush the younger lowers them repealy, even when it's cuckoo. Bush Sr. didn't invade Iraq beyond the UN resolutions, so Bush the younger flouts the UN and invades the country. Bush Sr. refu Saddam Hussein for invading a country and Bush the younger emula him by invading against international law. It's not as complica as you put it Jim Ferry, as it's just a rather dysfunctional family playing out its issues on the world stage. It's happened before, I'm sure. > But George Bush is simpleminded, so perhaps we should forgive him his > simplistic viewpoint. Hatred for America is engendered by . . . America's > better teeth. Now here's what I want you to do . . . Only a suggestion, > mind you: I'm all for freedom and human rights and democracy (my ideas > are also better than yours), so do whatever you want. What? What are you > doing? Now I have to beat the crap out of you! Oh, boo hoo, you want > your natural resources back? Too late, I ate them. Ha ha. Hey! Don't > hit me there! Evil terrorist! I have a date with Brittany Spears tonight! Bush isn't simpleminded and in fact he's quite intelligent, but lazy. I think part of what he does is out of anger at his father, and the rest is just following along with Cheney, who appears to be, um, not quite sane. > I'm not saying that you've installed any puppet dictatorships, James, but > there are aspects to America's foreign policy arrogance that remind me of > you. Sure, it's a natural reaction to being better than everyone else. > Better at building weapons, better at doing math, easy to think better in > every way. Easy to wonder, I'm so great, but they all hate me . . . they > must be wrong. They must be evil. Well Bush and I seem to have similarities, which I've noticed to my chagrin. I've decided that it comes from my being brought up as a fundamentalist Christian, so I understand that rigid thinking. > This is why I doubt that working out your Plan is even worth the effort. > No one likes being told they have to change their behavior to achieve their > goals. My guide (or muse, or the Holy Spirit, or whatever it is that seems > to be sending this Plan to me) argues that because you so fervently want to > achieve your goal and because you realize that what you're doing isn't > working, that you are receptive to new ideas. But I think your attitude is > more like, Let Ferry write his little plan, and if I don't like it, I'll > just laugh at it. So, yes, I'm resisting having to do this pointless work, > but still the Holy Spirit (or guide, or muse, or whatever) is prodding me on. Uh oh. Maybe I need to help you out a bit, in case you're losing it. Human beings are in the object ring. You're just a pack of ideas, in one sense. As ideas, you can be infec by ideas, like in the movie The Matrix. It turns out that very complex ideas, like human beings, exist in other forms, and they can infect a human mind. Thing is, such infections are rather hard to fix, as it's not so easy like in that movie. I'll consider your future replies Jim Ferry, and I may cut you loose. My suggestion, see someone, like a priest (not a Catholic priest), or even better, a Zen master. > So please, just tell me, Oh, you want me to roll over and play Mr. Nice > Guy! No dice! and then I can forget this whole hassle. At first I was so > honored that the Holy Spirit was choosing to work through me . . . oh, it's > probably a load of rubbish anyway. Me wanting to be important and imagining > that I was getting divine inspiration. The whole thing just seems ridiculous. > Never mind. I understand the feeling, and I take you seriously. You need to talk to someone, and not on Usenet. > Some of you are now facing the reality of the human brain versus any > fantasy you might have had about being completely rational. Human > beings are NOT rational creatures but necessarily rely on social > forces to determine what they believe. > You are creatures of society. > You may have believed that your mathematical knowledge was based > completely on logic and rationality, but human beings don't work that > way; it's built-in to your wiring NOT to work that way. > Some of you must learn to be more than human. > You know, I don't think genetics come into it. I'm in no position to > know, but here's what the little voice in my head says: > The chief difference between 's and the Establishment's > mathematical systems lies not in the validity of each: rather it is > simply that the world has chosen to accept the Establishment viewpoint. > Reality is crea by consciousness more than you know. > is attempting to create a new Reality to displace the old, but his > arguments simply *do not pertain* within the current Reality. The > current Reality is flawed, of course, by Goedelian indeterminancies, > and is ripe for replacement by something superior . . . Yop, you're infec Jim Ferry. > Yeah. Sounds like a load of crap. Like Langan's CTMU consciousness > creates the world crap. Forget it. > Mathematics is an absolute truth. Cbeck. That's Mathematics as opposed to mathematics. What most people call mathematics is a body of discoveries by people like me--discoverers. It can be flawed. But Mathematics is perfect. > The physical world is what it is. Check. The physical world is a finite bit of Mathematics. And like I said above, human beings are in the object ring. Yup, people, you are mathematical objects, just highly complica ones. > I apologize for all my inconsistencies. I star writing this in one > frame of mind, and ended up in another. A little voice in my head > telling me how can conquer the (mathermatical) world? > People are going to start telling *me* to take my meds . . . Go to a Zen master. A good one can handle that mental virus you have. > You must learn to be truly rational, for the first times in your > lives. > So it's about time, as I wait, and wonder, how many of you can handle > the truth. > And how many of you prefer the fantasy which was the world you > believed in, which actually never exis, except in your > imaginations; your wishes for a nicer world, where your wishes matter. > > My imagination. Sigh. I'm sure that's all it was. Sorry for wasting > your time. Now that was interesting. Subject: Re: JSH: About time > Now that I've revealed the odd and you could say esoteric error in > core mathematics with such a short, and rather simple argument, the > issue now is how long until mathematicians decide that they'd rather > have correct mathematics versus the *belief* that they had been > perfect in keeping error out of the collec body of work that is > called mathematics. Really, I can not understand your work, not even the core error problem. > I apologize for replying in a public forum, but I've chosen, or been > guided, to work under certain constraints. The danger of e-mail is the > temptation to say different things to different people. It would be > better for me, professionally, to hide my support for you, but I refuse > to do it. > Don't worry about it, as I find I'm liking your posts. Actually, I > kind of got a kick out of some of your previous posts back when you > were insulting me. > My thinking is that you appreciate quality work when you see it. > Now for those who wonder, being rather pissed at my current > predicament, with *some* mathematicians--I have to remember not to > characterize all of them--lying about my work or running away from it, > I sent Jim Ferry and a testy email, where I informed them > I considered them to be runners as well, and I would chase them down > with the rest, by getting a computerized proof check of my work. > And I also told Ferry to look for a job outside of mathematics. > Now, I'm not so angry, and I think that maybe I shouldn't have sent > that email, but then again, it all revolves around the question of > whether or not Jim Ferry does understand the math. > My work is out there and rather easy to go over as can be seen at the > Hong Konk math site: See http://mathdb.math.cuhk.edu.hk/forum/e_show.php?msg=782 And I send people there because their allowal of the use of LaTeX > makes for a *much* better presentation, and given the *social* issues > I'm facing, I need all the help I can get. The social issues. Indeed. What help could I be to you with the > mathematical issues? Even herd mathematicians like Magidin are better > at math than I. The fact is, you don't *need* any help with the > mathematical issues. > Ah yes, rather prescient of you to emphasize need. > It seems to me that things are about to get interesting. > I'm still working on your Plan. I've very busy right now, but I'm > finding ways to make the time for it. It will take several weeks > at least. As I began to conceive/receive it, I realized that it > would do no good if you had a Bush-like outlook on life. You seemed > annoyed by my detour into politics, but this is what I mean: you > being concerned with *mathematical* issues is like Bush trying to > build bigger bombs to fight terrorism. America is already powerful > enough, and doesn't need to become all-mighty so that all nations of > the world cower at the thought of incurring its wrath. According to > Bush, terrorists and the people who cheer for them are insane and evil. > According to Bush, a vast segment of the Islamic world is insane and evil. > Bush is having issues with his father, so he reversed his father on > everything. > Bush Sr. said he wouldn't raise taxes and did. So Bush the younger > lowers them repealy, even when it's cuckoo. > Bush Sr. didn't invade Iraq beyond the UN resolutions, so Bush the > younger flouts the UN and invades the country. > Bush Sr. refu Saddam Hussein for invading a country and Bush the > younger emula him by invading against international law. > It's not as complica as you put it Jim Ferry, as it's just a rather > dysfunctional family playing out its issues on the world stage. > It's happened before, I'm sure. > But George Bush is simpleminded, so perhaps we should forgive him his > simplistic viewpoint. Hatred for America is engendered by . . . America's have > better teeth. Now here's what I want you to do . . . Only a suggestion, > mind you: I'm all for freedom and human rights and democracy (my ideas > are also better than yours), so do whatever you want. What? What are you > doing? Now I have to beat the crap out of you! Oh, boo hoo, you want > your natural resources back? Too late, I ate them. Ha ha. Hey! Don't > hit me there! Evil terrorist! I have a date with Brittany Spears tonight! > Bush isn't simpleminded and in fact he's quite intelligent, but lazy. > I think part of what he does is out of anger at his father, and the > rest is just following along with Cheney, who appears to be, um, not > quite sane. > I'm not saying that you've installed any puppet dictatorships, James, but > there are aspects to America's foreign policy arrogance that remind me of > you. Sure, it's a natural reaction to being better than everyone else. > Better at building weapons, better at doing math, easy to think better in > every way. Easy to wonder, I'm so great, but they all hate me . . . they > must be wrong. They must be evil. > Well Bush and I seem to have similarities, which I've noticed to my > chagrin. > I've decided that it comes from my being brought up as a > fundamentalist Christian, so I understand that rigid thinking. > This is why I doubt that working out your Plan is even worth the effort. > No one likes being told they have to change their behavior to achieve their > goals. My guide (or muse, or the Holy Spirit, or whatever it is that seems > to be sending this Plan to me) argues that because you so fervently want to > achieve your goal and because you realize that what you're doing isn't > working, that you are receptive to new ideas. But I think your attitude is > more like, Let Ferry write his little plan, and if I don't like it, I'll > just laugh at it. So, yes, I'm resisting having to do this pointless work, > but still the Holy Spirit (or guide, or muse, or whatever) is prodding me on. > Uh oh. Maybe I need to help you out a bit, in case you're losing it. > Human beings are in the object ring. > You're just a pack of ideas, in one sense. > As ideas, you can be infec by ideas, like in the movie The > Matrix. > It turns out that very complex ideas, like human beings, exist in > other forms, and they can infect a human mind. > Thing is, such infections are rather hard to fix, as it's not so easy > like in that movie. > I'll consider your future replies Jim Ferry, and I may cut you loose. > My suggestion, see someone, like a priest (not a Catholic priest), or > even better, a Zen master. > So please, just tell me, Oh, you want me to roll over and play Mr. Nice > Guy! No dice! and then I can forget this whole hassle. At first I was so > honored that the Holy Spirit was choosing to work through me . . . oh, it's > probably a load of rubbish anyway. Me wanting to be important and imagining > that I was getting divine inspiration. The whole thing just seems ridiculous. > Never mind. > I understand the feeling, and I take you seriously. You need to talk > to someone, and not on Usenet. > Some of you are now facing the reality of the human brain versus any > fantasy you might have had about being completely rational. Human > beings are NOT rational creatures but necessarily rely on social > forces to determine what they believe. You are creatures of society. You may have believed that your mathematical knowledge was based > completely on logic and rationality, but human beings don't work that > way; it's built-in to your wiring NOT to work that way. Some of you must learn to be more than human. You know, I don't think genetics come into it. I'm in no position to > know, but here's what the little voice in my head says: The chief difference between 's and the Establishment's > mathematical systems lies not in the validity of each: rather it is > simply that the world has chosen to accept the Establishment viewpoint. > Reality is crea by consciousness more than you know. James Harris > is attempting to create a new Reality to displace the old, but his > arguments simply *do not pertain* within the current Reality. The > current Reality is flawed, of course, by Goedelian indeterminancies, > and is ripe for replacement by something superior . . . > Yop, you're infec Jim Ferry. > Yeah. Sounds like a load of crap. Like Langan's CTMU consciousness > creates the world crap. Forget it. Mathematics is an absolute truth. Cbeck. > That's Mathematics as opposed to mathematics. > What most people call mathematics is a body of discoveries by people > like me--discoverers. > It can be flawed. But Mathematics is perfect. > The physical world is what it is. Check. > The physical world is a finite bit of Mathematics. > And like I said above, human beings are in the object ring. > Yup, people, you are mathematical objects, just highly complica > ones. > I apologize for all my inconsistencies. I star writing this in one > frame of mind, and ended up in another. A little voice in my head > telling me how can conquer the (mathermatical) world? People are going to start telling *me* to take my meds . . . > Go to a Zen master. A good one can handle that mental virus you have. > You must learn to be truly rational, for the first times in your > lives. So it's about time, as I wait, and wonder, how many of you can handle > the truth. And how many of you prefer the fantasy which was the world you > believed in, which actually never exis, except in your > imaginations; your wishes for a nicer world, where your wishes matter. > My imagination. Sigh. I'm sure that's all it was. Sorry for wasting > your time. > Now that was interesting. > James, What do you expect to accomplish with all these insults you're dishing out? Not like you'll answer me anyway. These insults are childish, grow up. Subject: Re: JSH: About time >>Now that was interesting. >> > James, What do you expect to accomplish with all these insults you're > dishing out? Not like you'll answer me anyway. These insults are childish, > grow up. > ??? Were you and I reading the same post? James reply was insightful and fascinating. Sure, he and I disagree on a few points, but I don't understand how you could categorize it as insulting. It was actually quite helpful to me in my distress. Maybe James's and my upbringings are the root of some of our differences of opinion. James was brought up in a fundamentalist Christian household; my household was a jumble of various and/or no beliefs. My struggle is to find attunement with God in an empty, profane world. James probably has to work to shut out that oppressive, thundering, Old Testament Jehovah. Thus, whereas I welcome an inspiration of the Holy Spirit as fresh air, James seems to see such things as infections, mental diseases. Now that I see where you're coming from, James, let me say that I'm not oppressed by thunder, nor looking to be cured. Rather, I'm straining to hear something like far off music, like elven-song, and am amazed that I can still hear it if I try. I fear that it will abandon me if I fail to honor it, and that it would be a terrible shame to waste it. Though it merely moves through me toward you, when it moves through me, I am purified. I see now that it comes to me because you could never hear it, perhaps because of Jehovah's thunder, but more simply because of the hammer and tongs of your mathworks. Subject: Re: JSH: About time >[...] >James, What do you expect to accomplish with all these insults you're >dishing out? It's an interesting question. Sometimes I think that he's actually going to get people to agree he's right this way: You're wrong. Idiot. Well, you're still wrong. Liar. No, agreeing you were right would be lying. Satan's going to kill you. Oh my, I just can't tolerate these insults! Ok, you're right. I mean it's hard to believe anyone could think that it's going to work out that way, but he does believe lots of things that it's hard to believe anyone would believe... >Not like you'll answer me anyway. These insults are childish, >grow up. > ************************ Subject: Re: JSH: About time >>[...] >>James, What do you expect to accomplish with all these insults you're >>dishing out? >It's an interesting question. Sometimes I think that he's actually >going to get people to agree he's right this way: >You're wrong. >Idiot. >Well, you're still wrong. >Liar. >No, agreeing you were right would be lying. >Satan's going to kill you. >Oh my, I just can't tolerate these insults! Ok, you're right. >I mean it's hard to believe anyone could think that it's going >to work out that way, but he does believe lots of things that >it's hard to believe anyone would believe... But that's [bullying until somebody cried Uncle] is a successful tactic among children. Most^W[sigh!]some people figure out this doesn't work to one's advantage when they attain adulthood. It is bothersome that elementary schooling encourages this kind of persistent behaviour; teachers aren't supposed to correct mistakes because that may bruise the little egos and not build their confidence. /BAH Subtract a hundred and four for e-mail. Subject: Re: JSH: About time > >[...] > >James, What do you expect to accomplish with all these insults you're >dishing out? > It's an interesting question. Sometimes I think that he's actually > going to get people to agree he's right this way: > You're wrong. > Idiot. > Well, you're still wrong. > Liar. > No, agreeing you were right would be lying. > Satan's going to kill you. > Oh my, I just can't tolerate these insults! Ok, you're right. > I mean it's hard to believe anyone could think that it's going > to work out that way, but he does believe lots of things that > it's hard to believe anyone would believe... >Not like you'll answer me anyway. These insults are childish, >grow up. > > ************************ > Sometimes I wonder what his mathematical background is. He strikes me as someone who has had very little. If he actually has a physics degree, you would think that there'd be enough math there to set him straight; I'm a physics major myself (Meteorology). Subject: Re: JSH: About time > Sometimes I wonder what his mathematical background is. He strikes me as > someone who has had very little. If he actually has a physics degree, you > would think that there'd be enough math there to set him straight; I'm a > physics major myself (Meteorology). You can see that he doesn't get it at all if you mention anything that isn't simple arithmetic or that he hasn't defined himself. I'd say his mathematical background is extremely limi. The fact that he is completely unwilling (incapable?) of learning makes things worse. Subject: Re: JSH: About time >> >>[...] >> >>James, What do you expect to accomplish with all these insults you're >>dishing out? >> It's an interesting question. Sometimes I think that he's actually >> going to get people to agree he's right this way: >> You're wrong. >> Idiot. >> Well, you're still wrong. >> Liar. >> No, agreeing you were right would be lying. >> Satan's going to kill you. >> Oh my, I just can't tolerate these insults! Ok, you're right. >> I mean it's hard to believe anyone could think that it's going >> to work out that way, but he does believe lots of things that >> it's hard to believe anyone would believe... >>Not like you'll answer me anyway. These insults are childish, >>grow up. >> >> ************************ >> >Sometimes I wonder what his mathematical background is. None even though he might have received As in el-hi. I have a nephew who has been told all his young life that he knows a lot about computers. He knows nothing except how to point and click very fast. He has grown up thinking he knows it all just because he knew how to maniputate a mouse quickly. > .. He strikes me as >someone who has had very little. If he actually has a physics degree, you >would think that there'd be enough math there to set him straight; I'm a >physics major myself (Meteorology). My father claims he majored in history. His highest education level is 12th grade. When I went to high school, they also used the major word. It has nothing to do with the discipline associa with university terms. I suspect that some people may equate a high school major with a college-level degree. Did he really say physics degree or did you extrapolate that from him saying physics major? /BAH Subtract a hundred and four for e-mail. Subject: Re: JSH: About time > My father claims he majored in history. His highest education level > is 12th grade. When I went to high school, they also used the > major word. It has nothing to do with the discipline associa > with university terms. I suspect that some people may equate > a high school major with a college-level degree. Did he really > say physics degree or did you extrapolate that from him saying > physics major? He claims to have a BS in Physics from Vanderbilt. I give him the benefit of the doubt on that. I can assure you that you can get a BS in physics without ever seeing math at a very abstract level. He also was apparently in gif-talen programs as a youngster and had a lot of people telling him how smart he was. He seems unable to comprehend that a lot of the people in the newsgroups he frequents had the same life experiences, but managed to make the transition from big fish in little pond to little fish in big pond which, from all evidence, he did not. - Randy Subject: Re: JSH: About time > He also was apparently in gif-talen programs as a > youngster and had a lot of people telling him how smart > he was. He seems unable to comprehend that a lot of the > people in the newsgroups he frequents had the same life > experiences, but managed to make the transition from big fish > in little pond to little fish in big pond which, from > all evidence, he did not. Maybe he made a different transition. Out of the water . . . Subject: Re: JSH: About time > >[...] > >James, What do you expect to accomplish with all these insults you're >dishing out? > It's an interesting question. Sometimes I think that he's actually > going to get people to agree he's right this way: > You're wrong. > Idiot. > Well, you're still wrong. > Liar. > No, agreeing you were right would be lying. > Satan's going to kill you. > Oh my, I just can't tolerate these insults! Ok, you're right. > I mean it's hard to believe anyone could think that it's going > to work out that way, but he does believe lots of things that > it's hard to believe anyone would believe... >Not like you'll answer me anyway. These insults are childish, >grow up. > > ************************ > >>Sometimes I wonder what his mathematical background is. >None even though he might have received As in el-hi. I have >a nephew who has been told all his young life that he >knows a lot about computers. He knows nothing except how >to point and click very fast. He has grown up thinking he >knows it all just because he knew how to maniputate a mouse >quickly. Presumably he doesn't know how to find usenet... >> .. He strikes me as >>someone who has had very little. If he actually has a physics degree, you >>would think that there'd be enough math there to set him straight; I'm a >>physics major myself (Meteorology). >My father claims he majored in history. His highest education level >is 12th grade. When I went to high school, they also used the >major word. It has nothing to do with the discipline associa >with university terms. I suspect that some people may equate >a high school major with a college-level degree. Did he really >say physics degree or did you extrapolate that from him saying >physics major? He definitely has a degree in physics (or at least that's the story). Every once in a while it's explained that this is why we should believe he's right. >/BAH >Subtract a hundred and four for e-mail. ************************ Subject: Re: JSH: About time > >> >> >>[...] >> >>James, What do you expect to accomplish with all these insults you're >>dishing out? It's an interesting question. Sometimes I think that he's actually >> going to get people to agree he's right this way: You're wrong. >> Idiot. >> Well, you're still wrong. >> Liar. >> No, agreeing you were right would be lying. >> Satan's going to kill you. >> Oh my, I just can't tolerate these insults! Ok, you're right. I mean it's hard to believe anyone could think that it's going >> to work out that way, but he does believe lots of things that >> it's hard to believe anyone would believe... >> >>Not like you'll answer me anyway. These insults are childish, >>grow up. >> >> >> ************************ > >Sometimes I wonder what his mathematical background is. > None even though he might have received As in el-hi. I have > a nephew who has been told all his young life that he > knows a lot about computers. He knows nothing except how > to point and click very fast. He has grown up thinking he > knows it all just because he knew how to maniputate a mouse > quickly. > .. He strikes me as >someone who has had very little. If he actually has a physics degree, you >would think that there'd be enough math there to set him straight; I'm a >physics major myself (Meteorology). > My father claims he majored in history. His highest education level > is 12th grade. When I went to high school, they also used the > major word. It has nothing to do with the discipline associa > with university terms. I suspect that some people may equate > a high school major with a college-level degree. Did he really > say physics degree or did you extrapolate that from him saying > physics major? > /BAH > Subtract a hundred and four for e-mail. I remember him saying he had a physics degree, however, I could claim I have a math degree and you wouldn't know; that's the internet for you. By the way I don't have a math degree. Subject: qual vs quan research boundary=----=_NextPart_000_0034_01C391E6.5E7AD640 -------------------------------------------------------------- ------- charset=iso-8859-1 #1 - Is environmental dumping more likely to occur in impoverished neighborhoods compared to middle neighborhoods? (I think thit is quantative question) #2 - Do children raised in single parent families have greater academic difficulties than children raised in two parent families? (I think thit is quantative question) #3 - How does motivation lead to success in the workforce? (I think thit is qualatative question) Subject: Re: qual vs quan research > following questions and have to state whether they are qualatative or > quantative. HEre are the questions and what I think they are. Can anyone > tell me if I'm correct? THANKS! > #1 - Is environmental dumping more likely to occur in impoverished > #neighborhoods compared to middle neighborhoods? (I think thit is > #quantative question) > #2 - Do children raised in single parent families have greater academic > #difficulties than children raised in two parent families? (I think thit > #is quantative question) > #3 - How does motivation lead to success in the workforce? (I think thit > #is qualatative question) -- I'm not speaking as an expert here but this is what I think. Third is definately qualitative. The first two could be considered quantitative because the contain comparative words like more but I consider them qualitative because they are really questions of cause. Nobody really cares whether more or less of something happens here or there by accident. Any satisfactory answer to these questions would have to suggest a reason why more or less of something happens here or there. Besides, for a quantitative question, I would expect something more specific than more or less. I would expect an equation or something. Have a tolerable existence. Eli Subject: Re: Minimal Graph, Four Color Theorem I'd hesitate to ask you to go there, but it's Harris Steven James' 10-year program to prove the last theorem of Fermat. of course, it was actually his first one! he's wroking on the definition of divisibility, now. > I hesitate to ask, but what is HSJ? --les ducs de Enron! http://larouchepub.com Subject: Re: Quadratic System Help from slick_shoes@punkass.com: >18=a(5)^2+b(5)+c >69=a(12)^2+b(12)+c >74=a(14)^2+b(14)+c > I'm not sure how to go about solving this. In class, we've only solved >systems like this when on of the equations had x=0, so it rather easy to >solve for c. Can anybody point me in the right direction on this one? > >slick_shoes My earlier response never entered the newgroup, so I try again: You have three equations and three unknown values, now a, b, and c. If you understand a little about matrices, then you already can figure out what..... but you are asking for help, so you probably know at most, parts of intermediate algebra. If this is so, then either use an equation to find expression of one variable in terms of the others and back substitute; or use elimination by adding or subtracting multiples of one equation to another. G C Subject: Re: Quadratic System Help > from slick_shoes@punkass.com: >18=a(5)^2+b(5)+c >69=a(12)^2+b(12)+c >74=a(14)^2+b(14)+c I'm not sure how to go about solving this. One way is as a system of linear equations in a,b,and c as unknowns. 25*a + 5*b + c = 18 144*a + 12*b + c = 69 196*a + 14*b + c = 74 Another is by row reduction of the augmen matrix [[ 25 5 1 18 ] [ 144 12 1 69 ] [ 196 14 1 74 ]] Subject: harmonic functions How do you prove: Suppose D is a connec domain and {f_n} is a sequence of non-negative harmonic functions on D. Then we have one the following: (1) The sequence {f_n} contains a subsequence diverging to infinitely pointwise on D, (2) The sequence {f_n} contains a subsequence converging uniformly on compact subsets of D. My intuition is that all that is needed is Harnack's inequality (in one form or another) and the Arzela-Ascoli theorem, but I can't seem to combine them in just the right way... Subject: Re: harmonic functions >How do you prove: >Suppose D is a connec domain and {f_n} is a sequence of non-negative >harmonic functions on D. Then we have one the following: >(1) The sequence {f_n} contains a subsequence diverging to infinitely >pointwise on D, >(2) The sequence {f_n} contains a subsequence converging uniformly on >compact subsets of D. >My intuition is that all that is needed is Harnack's inequality (in one form >or another) and the Arzela-Ascoli theorem, but I can't seem to combine them >in just the right way... The fact that you seem to know what's needed to prove this makes it smell like homework - you can't quite figure out how to use the hint. So I'll give a few more hints: First, a relevant form of Harnack's inequality would be this: For any compact set K in D and any point p in D there is a constant c such that u(x) <= c u(p) for all x in K. Second, either the family is unbounded at some point or it isn't. Third, if K1, K2 are compact and K1 is contained in the interior of K2 then there exists c such that the sup of grad(u) over K1 is less than c times the sup of u over K2. (Note that bounds on grad(u) imply equicontinuity...) ************************ Subject: inversion via lagrange theory is it possible to invert something of a form say... f(t) = G(f(t)) + H(f(t),t) (G, H arbitrary functions, where as shown, H is explicitly dependant on t.) via say the lagrange inversion theorem to solve for f(t) ? (im not too familiar with the theorem, which is why i am asking...however on inspection of the theorem i would assume it is not possible....is there a theorem that allows for its solution?) cheers moth Subject: Re: Value of PI using trigonometry and calculus yess, thats pure calculus way to prove !! in my earlier post same has been proved using geometry too. atul > pi = lim n*sin(180/n) > n->inf lim(n->oo) n*sin 180/n = 180 lim(n->oo) (sin 180/n)/(180/n) > = 180 lim(x->0) (sin x)/x > = 180 provided x is in radians > I believe this thing is known and exists. Basic calculus > lim(x->0) (sin x)/x = 1 Subject: Re: Value of PI using trigonometry and calculus William, What I was saying, was correct. Finally I found it in one of the answers on Dr. Math website. It reads as follows : Subject: Re: Pi and Polygons This method of finding successive approximations to Pi is one of the oldest methods known, because it is one of the easiest to understand, and you can draw nice pictures to explain it. If a regular polygon has n sides, then we can draw lines from its center to all the vertices, and these lines will divide the pie-shaped picture into n wedges. Each wedge's central angle will have a measure of 360/n degrees. So, we can draw this picture of one wedge, where C is at the center of the polygon: A /| / | / | / | / | C /__________| D | | | | | | B Segment AB here is one side of the original regular polygon. Since angle ACB is 360/n, angle ACD is 180/n. Therefore, if the length of AC is 1/2, the length of AD is sin(180/n)/2. Therefore, the length of AB is sin(180/n), and the perimeter of the entire polygon is n*sin(180/n). So, you are correct: when you let n go toward infinity, sin(180/n) will tend towards zero. Since we know that a circle whose radius is 1/2 has a circumference of Pi, the 0 and infinity balance each other in the limit. Of course, there is a practical problem with all of this. In order to calculate the sines, you need to know a thing or two about Pi. It is true that for some special angles like 30, 45, and 60 degrees (and their sums and differences, etc.) you can write down an explicit elementary expression for their sines, this is not true of some other angles like 180/11. So, how do we calculate the perimeters without knowing Pi already? We need to find some trick, or we need to find some other method entirely of approximating Pi. And that is where a great part of the glorious history of mathematics starts. For more about Pi, its role in history, and the various attempts to know it better, check out the excellent book _A History of Pi_ by Petr Beckmann. People have done some pretty clever things to get to know Pi. - Doctor Ken, The Math Forum http://mathforum.org/dr.math/ Atul > pi = lim n*sin(180/n) > n->inf lim(n->oo) n*sin 180/n = 180 lim(n->oo) (sin 180/n)/(180/n) > = 180 lim(x->0) (sin x)/x > = 180 provided x is in radians > I believe this thing is known and exists. Basic calculus > lim(x->0) (sin x)/x = 1 Subject: JVC Anyone who knows the difference between the Jonker Volgenant (JV) and the Jonker Volgenant Castanion (JVC) Algorithm? Subject: Re: Groups with 16 elements in message <70ae81fd.0310131215.7298be0@posting.google.com>: > I found an interesting program for doing things > with groups of order < 32 at http//math.ucsd.edu/~jwavrick . > program (or using telnet); [...] > ORDERS for Groups Number 35 and 38 > Group number 35 of Order 16 > 1 elements of order 1: A > 3 elements of order 2: C E G > 12 elements of order 4: B D F H I J K L M N O P > 0 elements of order 8: > 0 elements of order 16: > Both 35 and 38 have the same center; Z = {A E C G}. > This is the same distribution of orders as in Z_2 x Q, so > 35 or 38 is Z_2 x Q. > For 35 and 38, there are 6 = 12/2 elements of order 4, You mean 6 *cyclic subgroups* of order 4, not 6 elements. > and if we call these x_i; i=1,6, then let > x_1^2 = x_2^2, x_3^2 = x_4^2, x_5^2 = x_6^2, > which gives 3 elements of order 2, all of which are in the center. No. All elements of order 4 in Z_2 x Q square to the same element, so 2 of the 3 involutions in the center are not the square of an element of order 4. Likewise, only 2 of the 3 involutions in the center of the other non-abelian group with this distribution of element orders are the squares of elements of order 4. This group is the semidirect product Z_4 x| Z_4 with presentation . > ========= > I would like to look first at the 5 groups 34 thru 38 groups more > closely. (Note that none of these 5 have an element of order 8.) > Also, #36 and 37 have the same distribution of orders. > ORDERS for Group Number 36 > Group number 36 of Order 16 > 1 elements of order 1: A > 7 elements of order 2: C E G I K N P > 8 elements of order 4: B D F H J L M O > 0 elements of order 8: > 0 elements of order 16: > ORDERS for Group Number 37 > Group number 37 of Order 16 > 1 elements of order 1: A > 7 elements of order 2: C E G I K M O > 8 elements of order 4: B D F H J L N P > 0 elements of order 8: > 0 elements of order 16: > CENTER of Group Number 36 { A B C D } (cyclic--Z_4) > CENTER of Group Number 37 { A C E G } (Z_2 x Z_2) [...] > This shows the structure of 36, but I haven't figured out how to > write it concisely, as one does for D_8, e.g. This is the central product Z_4 * D_4 =~ Z_4 * Q that Derek mentioned. It has rank 3, and one easy presentation is . Group 37 has rank 2 with, for example, presentation . > I plan to look at the rest of the groups. I don't yet see > how one decides how many groups there are with each distribution of > orders. It didn't turn out quite like I thought--there are more > groups with no element of order 8 than I would have guessed. I know of no way to decide except to actually construct all of the groups of order 16 and count the elements of each order in each group. > There must be a systematic way of doing this--I know there are > papeand I think some books, on groups of order 2^n, but > I am not at a University, so I don't have the easy access > that I used to have. As I pos earlier in the thread, the systematic way is to look for all possible ways that 2 subgroups of order 8 can intersect, necessarily in a subgroup of order 4, such that one normalizes the other. You correctly star on this path when you looked at all the ways to have a cyclic subgroup of order 8. -- Jim Heckman Subject: Re: JSH: $100,000 US offer, Abel Prize > Tee-hee. Nothing makes a pig happier than a roll in the wallow, as this tittering porker knows! http://www.shop4egifts.com/target.asp?item=/jpg/25112.jpg& width=314&height=4 00# > Heh-heh. Nothing makes a donkey happier than a rut in the barnyard, as this hee-hawing hoofer knows. http://www.rubylane.com/ni/shops/viperswife/iteml/GW-684 > Subject: abstract math I was wondering if I could get some help on this problem. We know that multiplication of integers is commutative; i.e. ab=ba for all pairs of integers a and b. Prove that, for every natural number n, the product of n integers is independant of the order of the factors. Thanks. Subject: Re: abstract math >I was wondering if I could get some help on this problem. >We know that multiplication of integers is commutative; i.e. ab=ba for >all pairs of integers a and b. Prove that, for every natural number n, >the product of n integers is independant of the order of the factors. This requires associative as well. If f(a,b) = (a+b)^2, this operation is commutative but not associative, and it is false, as f(1, f(1, 3)) = (1 + 10)^2, and f(f(1,1), 3) = (4 + 3)^2. For commutative and associative operations, it is an exercise in induction. -- 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: abstract math > I was wondering if I could get some help on this problem. > We know that multiplication of integers is commutative; i.e. ab=ba for > all pairs of integers a and b. Prove that, for every natural number n, > the product of n integers is independant of the order of the factors. Hint: Given any permutation of ABC... normalize it by first moving A to the first place via transpositions then inductively doing the same on the tail after A, moving B to the 2nd place, C to the third place, etc. e.g. DCBA DCAB DACB ADCB now A is in normal place, work on rest DBC BDC now B is in normal place, work on rest CD now C is in normal place, so too is D ---- ABCD If you've studied permutation groups you'll recognize the relationship to the representation of a permutation as a product of transpositions. -Bill Dubuque Subject: Re: abstract math >We know that multiplication of integers is commutative; i.e. ab=ba for >all pairs of integers a and b. Prove that, for every natural number n, >the product of n integers is independant of the order of the factors. I hate this type of homework: it is more difficult to neatly write down what it is that you have to prove [*] than to actually prove it. [*] For all natural numbers n, for all integers x_1,...,x_n, for all bijections f : {1,...,n} -> {1,...,n} x_1 * x_2 * ... * x_n = x_f(1) * x_f(2) * ... * x_f(n) and even then I should probably make clear where the parethesis are supposed to be in the products. Peter van Rossum Subject: Re: abstract math > I was wondering if I could get some help on this problem. > We know that multiplication of integers is commutative; i.e. ab=ba for > all pairs of integers a and b. Prove that, for every natural number n, > the product of n integers is independant of the order of the factors. > Thanks. Mathematical Induction and the UFT. Bob Pease Subject: Re: abstract math >> I was wondering if I could get some help on this problem. >> We know that multiplication of integers is commutative; i.e. ab=ba for >> all pairs of integers a and b. Prove that, for every natural number n, >> the product of n integers is independant of the order of the factors. >> Thanks. > Mathematical Induction and the UFT. You don't need unique factorization. The property holds in any commutative ring, not just in a UFD. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. Subject: Re: abstract math Amin schrieb im Newsbeitrag > I was wondering if I could get some help on this problem. > We know that multiplication of integers is commutative; i.e. ab=ba for > all pairs of integers a and b. Prove that, for every natural number n, > the product of n integers is independant of the order of the factors. > Thanks. Sorry for asking: But why would you want to prove this? I mean - I believe in it, that's enough for me. Don't want to offend you - I was just currious. -Gernot Subject: Re: abstract math > Amin schrieb im Newsbeitrag I was wondering if I could get some help on this problem. We know that multiplication of integers is commutative; i.e. ab=ba > for > all pairs of integers a and b. Prove that, for every natural number > n, > the product of n integers is independant of the order of the > factors. Thanks. > Sorry for asking: But why would you want to prove this? I mean - I > believe in it, that's enough for me. > Don't want to offend you - I was just currious. > -Gernot It is not so much offensive as indicative of potentially dangerous Snerdism. Would you post a message like this to a newsgroup like alt.religion.Christian? Sorry for asking: But why would you want to believe this? I mean - I believe in God, that's enough for me. Don't want to offend you - I was just currious. The CENTRAL reason for studying Math is to DO proofs. Whazzamatta you??? RJ Pease Subject: Re: abstract math > The CENTRAL reason for studying Math is to DO proofs. I would just like to quote Laurent Schwartz : The reason for studying math is to discover some interesting properties, and to prove them just to be sure. Well, I would consider proofs as mere tools... Yann Subject: Re: abstract math > Amin schrieb im Newsbeitrag I was wondering if I could get some help on this problem. We know that multiplication of integers is commutative; i.e. ab=ba > for > all pairs of integers a and b. Prove that, for every natural number > n, > the product of n integers is independant of the order of the > factors. Thanks. > Sorry for asking: But why would you want to prove this? I mean - I > believe in it, that's enough for me. > Don't want to offend you - I was just currious. It's a standard approach in mathematics: Start from as few axioms as possible, and build things up. In this case, it shows you don't need to take equivalence of arbitrary permutation as an axiom, you just need to take commutation of pairs. And, I believe, associativity. To the OP: Try induction on n. Consider this at the induction step: (product of n-1 factors)*x Now, from your assumptions, you can do two thing without changing the product: - interchange x and the last element in (product of n-1 factors) - rearrange (product of n-1 factors) in any way you like. Can you convince yourself (and your teacher) that these two operations are sufficient to generate all permutations of n factors? Try it for 3 or 4 factors. If that's not sufficient, note that you can also do this operation: - regroup as (first factor)*(n-2 factors * x) and this: - regroup as (first factor)*(any permutation of n-2 factors and x) - Randy Subject: Re: abstract math >Amin schrieb im Newsbeitrag >> I was wondering if I could get some help on this problem. >> We know that multiplication of integers is commutative; i.e. ab=ba for >> all pairs of integers a and b. Prove that, for every natural number n, >> the product of n integers is independant of the order of the factors. >Sorry for asking: But why would you want to prove this? I mean - I >believe in it, that's enough for me. >Don't want to offend you - I was just currious. This is only a guess. Beginning of school year = beginning of home work in class writing proofs. Can't see the answer immediately = ask the net for the answer. More advanced math work = believes only what can be proven. Subject: Re: abstract math > I was wondering if I could get some help on this problem. > We know that multiplication of integers is commutative; i.e. ab=ba for > all pairs of integers a and b. Prove that, for every natural number n, > the product of n integers is independant of the order of the factors. > Thanks. Would an induction proof work? Bill Subject: Intersection area of 2 circles assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and radiuses r1, r2. Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the intersection's center of mass (if 2d can have mass), and the area of the intersection. Thank you very much. -- -Gernot In order to reply, revert my forename from: tonreG.Frisch.at.Dream-D-Sign.de@invalid.com ________________________________________ Looking for a good game? Do it yourself! GLBasic - you can do www.GLBasic.com Subject: Re: Intersection area of 2 circles > assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and > radiuses r1, r2. > Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the > intersection's center of mass (if 2d can have mass), and the area of > the intersection. Draw the common chord and all the radii to its endpoints. The area of the intersection is a sector minus an isosceles triangle on each side of the chord. Add 'em up. I can't think of a much slicker way to do the CoM than the same construction. It's not very hard to work out the CoM of a sector[1] and the CoM of a triangle is its centroid, then use linearity. [1] if the sector has radius r and angle 2t then I make the CoM a distance (2 sin t)/(3t) from the centre. But that's just a quick guess. > Thank you very much. You are welcome :) Dave -- Remove the opinion on spam to reply. Subject: Re: Intersection area of 2 circles >> assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and >> radiuses r1, r2. >> Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the >> intersection's center of mass (if 2d can have mass), and the area of >> the intersection. > Draw the common chord and all the radii to its endpoints. The area of the > intersection is a sector minus an isosceles triangle on each side of the > chord. Add 'em up. > I can't think of a much slicker way to do the CoM than the same > construction. It's not very hard to work out the CoM of a sector[1] and > the CoM of a triangle is its centroid, then use linearity. > [1] if the sector has radius r and angle 2t then I make the CoM a distance > (2 sin t)/(3t) from the centre. But that's just a quick guess. >> Thank you very much. > You are welcome :) > Dave I'm not certain, but I would think that the center of mass would be the average of the centers of the two circles weigh by their areas, that is, ( (x1,y1)*pi*r1^2 + (x2,y2)*pi*r2^2 ) / ( pi*r1^2 + pi*r2^2 ) Have a tolerable existence. Eli -- Subject: Re: Intersection area of 2 circles assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and >> radiuses r1, r2. >> Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the >> intersection's center of mass (if 2d can have mass), and the area of >> the intersection. Draw the common chord and all the radii to its endpoints. The area of > the intersection is a sector minus an isosceles triangle on each side > of the chord. Add 'em up. I can't think of a much slicker way to do the CoM than the same > construction. It's not very hard to work out the CoM of a sector[1] and > the CoM of a triangle is its centroid, then use linearity. [1] if the sector has radius r and angle 2t then I make the CoM a > distance (2 sin t)/(3t) from the centre. But that's just a quick guess. I'm not certain, but I would think that the center of mass would be the > average of the centers of the two circles weigh by their areas, that > is, ( (x1,y1)*pi*r1^2 + (x2,y2)*pi*r2^2 ) / ( pi*r1^2 + pi*r2^2 ) The center of mass of the intersection cannot be loca as you thought. Consider, for example, a degenerate case when one disk is completely contained within another disk of larger radius. Then the center of mass of the intersection is always just the center of the smaller disk; it is independent of the center and radius of the larger disk. David Cantrell Subject: Re: Intersection area of 2 circles assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and > radiuses r1, r2. > Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the > intersection's center of mass (if 2d can have mass), and the area of > the intersection. Draw the common chord and all the radii to its endpoints. The area of >> the intersection is a sector minus an isosceles triangle on each side >> of the chord. Add 'em up. I can't think of a much slicker way to do the CoM than the same >> construction. It's not very hard to work out the CoM of a sector[1] and >> the CoM of a triangle is its centroid, then use linearity. [1] if the sector has radius r and angle 2t then I make the CoM a >> distance (2 sin t)/(3t) from the centre. But that's just a quick guess. I'm not certain, but I would think that the center of mass would be the >> average of the centers of the two circles weigh by their areas, that >> is, ( (x1,y1)*pi*r1^2 + (x2,y2)*pi*r2^2 ) / ( pi*r1^2 + pi*r2^2 ) > The center of mass of the intersection cannot be loca as you thought. > Consider, for example, a degenerate case when one disk is completely > contained within another disk of larger radius. Then the center of mass > of the intersection is always just the center of the smaller disk; it is > independent of the center and radius of the larger disk. > David Cantrell You're right. Oh, well. Have a tolerable existence. Eli -- Subject: Re: Intersection area of 2 circles > assume 2 circles in 2D with given centers cx1, cy1 and cx2, cy2 and > radiuses r1, r2. > Now if dist(c1, c2) < r1+r2, the circles intersect. What I need is the > intersection's center of mass (if 2d can have mass), and the area of > the intersection. > Draw the common chord and all the radii to its endpoints. The area of the > intersection is a sector minus an isosceles triangle on each side of the > chord. Add 'em up. Or see formula (11) at . > I can't think of a much slicker way to do the CoM than the same > construction. It's not very hard to work out the CoM of a sector[1] and > the CoM of a triangle is its centroid, then use linearity. > [1] if the sector has radius r and angle 2t then I make the CoM a > distance (2 sin t)/(3t) from the centre. But that's just a quick guess. But of course that distance can't be independent of r. I suppose you intended to write (2 r sin t)/(3t); if so, your quick guess was correct. David Cantrell Subject: Re: should Gauss's Law of Magnetism be: Integral B dot dA = q/p + q/p_t > So the new Gauss Law of Magnetism looks somewhat like this: > Integral B dot dA = q/p + q/p_t where t is temperature rela. > This new law restores complete symmetry to the Maxwell Equations. It > dismisses the monopole idea completely. > It just says that we were just not advanced enough since the 1800s > when > the Gauss laws were built to realize that temperature and (probably > pressure as well) needs to be fit into the Maxwell Equation > structure. > As you can see, the q/p + q/p_t is algebraically equivalent to u i + u > i_d > and thereby we have *complete symmetry* within the Maxwell Equations. I suspect this new Gauss Law of Magnetism would need a negative term and that the q/p_t term should be negative. Makes sense in that the Meissner Effect is a exclusion of a magnetic field inside the entire volume. And this issue would suggest that Graham Lee is wrong when he says the Maxwell Eq. conform to the Meissner Effect because the Gauss Law of Magnetism really does not conform to the Meissner Effect in that there is nothing in the Maxwell Equations to give a exclusion of magnetism from all volume. So the Maxwell Equations do indeed have a large gap in that there is nothing in the Maxwell Equations to account for a exclusion of magnetism from volume. If the above new Gauss Law of Magnetism is correct, whether it has a negative term or not, then, it should predict other phenomenon. And although I do not have temperature (and perhaps pressure also) included, I should be able to cast some sort of prediction just on form alone. So, let us say this new Gauss law of Magnetism, either Integral B dot dA = q/p + q/p_t or Integral B dot dA = q/p - q/p_t was correct. Then what sort of new prediction would that law give? Well, it should give some prediction concerning normal conductivity in that the magnetism inside a normal conductor such as copper at room temperature. That the internal magnetism of the term ( - q/p_t ) does not exclude an outside magnet from its volume and thus that term represents what physically? I suspect it represents resistance to the current flow. So that perhaps resistance to current flow is all contained within a revised Maxwell theory. Which makes sense, because if the true Maxwell Equations have a temperature and pressure parametethen that translates into resistance. Archimedes Plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies Subject: predictions of a newly revised Gauss Law of Magnetism: Integral B dot dA = q/p - q/p_t Another prediction of this newly revised Gauss Law of Magnetism would be to give the numbers of the Quantized Hall Effect. And that makes sense on another level of logic. If I remember correctly, the algebraic form of spectral lines series such as Balmer or Rydberg follows a form such as this: 1/x - 1/y And this new Gauss law is not much different with its q/p - q/p_t and that makes alot of sense also in that spectral lines are not much different from Quantum Hall Effect, in fact, one can argue that the Quantum Hall Effect is spectral lines. So, if this above equation for Gauss Law of Magnetism is correct and true would predict that the math numbers that arise in Quantized Hall Effect should follow from this new equation. For we all know that superconductivity and Meissner Effect and Quantum Hall Effect are all linked. And going in the reverse direction of starting with Spectral line formulas, one should be able to derive a generalized Maxwell Equations, without ever knowing what they were at the outset. Archimedes Plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies Subject: Re: The Passing of a Mathematician >In which particular way does the NSA keep alive the value of democracy? It helps protect the Uni States of America, a democratic nation, from being invaded and conquered by foreign non-democratic nations. John Savard http://home.ecn.ab.ca/~jsavard/index.html Subject: Re: The Passing of a Mathematician > In which particular way does the NSA keep alive the > value of democracy? By protecting the security of the Uni States, a major democratic power, and its citizens. -- Transpose hotmail and mxsmanic in my e-mail address to reach me directly. Subject: Re: polysigned numbers > Using my notation of (-,+,*,#), there are two possible reductions for > (a,b,c,d). I presume that in this notation (*1)^2 = -1, (*1)(-1) = #1 and (*1)(#1) = +1 etc. > The tetrahedral interpretation uses: (a,b,c,d) = (a-m,b-m,c-m,d-m) where > m = min(a,b,c,d). > The tetrahedral maps to R^3, with no obvious interpretation of > multiplication (to me), and addition corresponds to vector addition of > (i,j,k) points. I didn't work out the mapping in detail since you > pos it elsewhere. If my assumption is correct these 4-signed numbers form a ring isomorphic to R x C: *1 will correspond to (-1, i) etc. -- Subject: Re: polysigned numbers >>Using my notation of (-,+,*,#), there are two possible reductions for >>(a,b,c,d). > I presume that in this notation (*1)^2 = -1, (*1)(-1) = #1 and (*1)(#1) = +1 > etc. > As Timothy has defined it, no. -1(a,b,c,d) = (d,a,b,c) +1(a,b,c,d) = (c,d,a,b) *1(a,b,c,d) = (b,c,d,a) #1(a,b,c,d) = (a,b,c,d) >>The tetrahedral interpretation uses: (a,b,c,d) = (a-m,b-m,c-m,d-m) where >>m = min(a,b,c,d). >>The tetrahedral maps to R^3, with no obvious interpretation of >>multiplication (to me), and addition corresponds to vector addition of >>(i,j,k) points. I didn't work out the mapping in detail since you >>pos it elsewhere. > If my assumption is correct these 4-signed numbers form a ring > isomorphic to R x C: *1 will correspond to (-1, i) etc. No. You'll have to apply trig functions to get the exact values. You are going from norm 1 to norm sqrt(2). The norm is preserved under the isomorphism. -- Will Twentyman email: wtwentyman at copper dot net Subject: Re: polysigned numbers >Using my notation of (-,+,*,#), there are two possible reductions for >(a,b,c,d). >> I presume that in this notation (*1)^2 = -1, (*1)(-1) = #1 and (*1)(#1) = >> +1 etc. >> > As Timothy has defined it, no. > -1(a,b,c,d) = (d,a,b,c) > +1(a,b,c,d) = (c,d,a,b) > *1(a,b,c,d) = (b,c,d,a) > #1(a,b,c,d) = (a,b,c,d) Bonkers: so #1 is the multiplicative identity not +1 :-( >The tetrahedral interpretation uses: (a,b,c,d) = (a-m,b-m,c-m,d-m) where >m = min(a,b,c,d). >The tetrahedral maps to R^3, with no obvious interpretation of >multiplication (to me), and addition corresponds to vector addition of >(i,j,k) points. I didn't work out the mapping in detail since you >pos it elsewhere. >> If my assumption is correct these 4-signed numbers form a ring >> isomorphic to R x C: *1 will correspond to (-1, i) etc. > No. Yes: Still isomorphic to R x C. > You'll have to apply trig functions to get the exact values. You > are going from norm 1 to norm sqrt(2). The norm is preserved under the > isomorphism. Sorry, that makes no sense? -- Subject: Re: polysigned numbers >>Using my notation of (-,+,*,#), there are two possible reductions for >>(a,b,c,d). >I presume that in this notation (*1)^2 = -1, (*1)(-1) = #1 and (*1)(#1) = >+1 etc. >As Timothy has defined it, no. >>-1(a,b,c,d) = (d,a,b,c) >>+1(a,b,c,d) = (c,d,a,b) >>*1(a,b,c,d) = (b,c,d,a) >>#1(a,b,c,d) = (a,b,c,d) > Bonkers: so #1 is the multiplicative identity not +1 :-( Correct. >>The tetrahedral interpretation uses: (a,b,c,d) = (a-m,b-m,c-m,d-m) where >>m = min(a,b,c,d). >> >>The tetrahedral maps to R^3, with no obvious interpretation of >>multiplication (to me), and addition corresponds to vector addition of >>(i,j,k) points. I didn't work out the mapping in detail since you >>pos it elsewhere. >If my assumption is correct these 4-signed numbers form a ring >isomorphic to R x C: *1 will correspond to (-1, i) etc. >>No. > Yes: Still isomorphic to R x C. >> You'll have to apply trig functions to get the exact values. You >>are going from norm 1 to norm sqrt(2). The norm is preserved under the >>isomorphism. > Sorry, that makes no sense? You're right, I had forgotten how multiplication in RxC works. So #1 = (1,1) What would -1,+1,*1 be? -- Will Twentyman email: wtwentyman at copper dot net Subject: Re: JSH your ship has come in!!!! > But, I expect you remember that I did ask you a question that I was unable > to answer. I was using the notation [a,b,c] to represent an ordered triple of complex > numbers. And I was wondering if the ordered triple [1,2,8] was an element of > the Object Ring. You replied: > ================================== > Quit being lazy!!! You have the definition, figure it out for yourself!!! > What amazes me is how often people are willing to ask someone else to do > their work for them. > If you're smart enough, answer your own question. > I'm curious to see if you can. > I've given the definition for the object ring, so no excuses. > ================================== Well, I am ashamed to say I still cannot figure it out. > Sounds like a ploy. James... I am having genuine problems with my question. I don't really see how it could be called a ploy. If you know the answer you could tell me, and put me out of my misery. If you don't know the answer, fair enough, you can't be expec to know everything. -- Clive Tooth http://www.clivetooth.dk Subject: Re: JSH your ship has come in!!!! interpre to mean that you are just humoring me. > Backtracked? After the initial jolt I went a little overboard, calling you the > messiah, etc. I've certainly backed off that stance. Please consider how > dizzying it is to be shaken out of the conventional mindset. You did? When? I thought you just had some wild and scary dream with me in a castle and stuff. Cool dream. Any more? > Well then, how about the core error problem? > Can't you understand how independent terms are independent? > I just don't get it! How many times do I have to tell you! Your > mathematical writings make no sense to me! Are you going to be calling me a > retard next? You are quite intelligent, and in fact are one of the most intelligent people, by your IQ, on the planet. So no, I will not call you a retard Jim Ferry, as you are not one. > Oh, excuuuuse me for not being as smart as you, James! What happens to me in > the New World Order? Do you send me to the slaughterhouse with all the other > meat animals? Huh? Look around you Jim Ferry. There's more than enough slaughter going on now to distress the cognizant, and I assure you that I'm not doing any of it. My efforts to try and prevent some of it, like my emails about Iraq's supposed weapons of mass destruction stockpiles, failed. Other efforts of mine have failed as well, and I've learned not to carry the world on my shouldenot even in fantasy. Sigh. I feel a bit guilty now. And I sent you that nasty email talking about putting you out of mathematics as well. Maybe there IS a problem with how I've gone about things. > Sure, I've got some trinkets of intellect: M.I.T. degree, some Putnam > medals, Ph.D. from Brown, joined Mega once, mathematician, rocket > scientist, etc. But that's a hell of long way from the serious hardware > that you're interes in: > Abel Prize, Fields Medal, Nobel Prize, Clay Prize, etc. And even the people > who have such hardware aren't necessarily able to follow in your bold > footsteps. > So why are you on *my* case? Because you *backtracked*!!! It would have been better if you'd said nothing at all!!! Now I have to toss you into the pile with Barry Mazur, Andrew Granville, Ralph McKenzie, David Ullrich, and . > I never claimed to understand your work. Maybe I had a fleeting flash of > intuition that it was correct, but that was all. Are you being honest Jim Ferry? Please explain to me why you ever claimed my work was correct *in detail*. I think you owe me that as I'm worried it was some kind of cruel prank. > I was offering a different kind of help. Something to complement and > complete the intense laser of your rational thought. Something to help > bring your theories into the human realm. You don't believe in the efficacy > of such things, I guess, or you just want to sear your way through with that > laser of youso fine. Go get 'em, tiger. You don't need my help. Actually I don't need your help, but I *would* appreciate it greatly. But how do I know if you're sincere, or just playing some elaborate joke? As for understanding my work, math proofs begin with a truth and proceed by logical steps to a conclusion which then must be true. I give you the steps, you follow, and then I'd think you should understand. Subject: Re: JSH your ship has come in!!!! >[...] >> I just don't get it! How many times do I have to tell you! Your >> mathematical writings make no sense to me! Are you going to be calling me a > retard next? >You are quite intelligent, and in fact are one of the most intelligent >people, by your IQ, on the planet. Just curious: How do you know anything about his IQ? >So no, I will not call you a retard Jim Ferry, as you are not one. >> Oh, excuuuuse me for not being as smart as you, James! What happens to me in >> the New World Order? Do you send me to the slaughterhouse with all the other >> meat animals? >Huh? Look around you Jim Ferry. There's more than enough slaughter >going on now to distress the cognizant, and I assure you that I'm not >doing any of it. >My efforts to try and prevent some of it, like my emails about Iraq's >supposed weapons of mass destruction stockpiles, failed. >Other efforts of mine have failed as well, and I've learned not to >carry the world on my shouldenot even in fantasy. Same hint as always: if you don't like it when... oh, never mind. >Sigh. I feel a bit guilty now. And I sent you that nasty email >talking about putting you out of mathematics as well. >Maybe there IS a problem with how I've gone about things. Giggle. Perhaps. >> Sure, I've got some trinkets of intellect: M.I.T. degree, some Putnam > medals, Ph.D. from Brown, joined Mega once, mathematician, rocket >> scientist, etc. But that's a hell of long way from the serious hardware >> that you're interes in: >> Abel Prize, Fields Medal, Nobel Prize, Clay Prize, etc. And even the people >> who have such hardware aren't necessarily able to follow in your bold >> footsteps. >> So why are you on *my* case? >Because you *backtracked*!!! >It would have been better if you'd said nothing at all!!! >Now I have to toss you into the pile with Barry Mazur, Andrew >Granville, Ralph McKenzie, David Ullrich, and . >> I never claimed to understand your work. Maybe I had a fleeting flash of >> intuition that it was correct, but that was all. >Are you being honest Jim Ferry? >Please explain to me why you ever claimed my work was correct *in >detail*. >I think you owe me that as I'm worried it was some kind of cruel >prank. For heaven's sake. Yes, when he says he doesn't understand your work but thinks it's correct he's joking. Regarding whether it's cruel: I would have never imagined in my wildest dreams that even _you_ could possibly be so blinded by megalomania and so desparate for approval that you'd think someone was being sincere when he says he doesn't understand your work but nonetheless thinks it's right. I mean that's such an _utterly_ ridiculous thing to say in a mathematical context that it's hard to see how anyone could possibly not take it as a joke. So I'm certain he assumed that you'd realize all along he was making fun of you. Making fun of you is perhaps a little nasty, but it's certainly no nastier than you deserve given your obnoxious nehavior for yeaso it doesn't bother me. But lately when you start talking like you think he's being sincere it becomes a whole different story. Actually encouraging a lunatic's delusions is not a nice thing to do. On the other hand the fact that you've thought he was sincere is _the_ most hilarious thing I've ever seen - we need to consider the greatest good of the greatest number and all that, being a little nasty to you versus people all over the planet laughing their asses off, I think it's a wash. Honest. I point this out just in case you might decide to try not to be _quite_ so hilarious: People have been laughing at Jim's parodies for yeabut lately when you seem to believe he's being sincere, or _might_ be sincere, in this and rela threads, it really does add a whole new dimension - goes from hilarious to absolutely world-class hilarious. Now you know. >> I was offering a different kind of help. Something to complement and >> complete the intense laser of your rational thought. Something to help >> bring your theories into the human realm. You don't believe in the efficacy >> of such things, I guess, or you just want to sear your way through with that >> laser of youso fine. Go get 'em, tiger. You don't need my help. >Actually I don't need your help, but I *would* appreciate it greatly. >But how do I know if you're sincere, or just playing some elaborate >joke? >As for understanding my work, math proofs begin with a truth and >proceed by logical steps to a conclusion which then must be true. >I give you the steps, you follow, and then I'd think you should >understand. > ************************ Subject: Re: JSH your ship has come in!!!! >>[...] >I just don't get it! How many times do I have to tell you! Your >mathematical writings make no sense to me! Are you going to be calling me a >retard next? >>You are quite intelligent, and in fact are one of the most intelligent >>people, by your IQ, on the planet. > Just curious: How do you know anything about his IQ? James is referring to the fact that I was able to join Mega, which purports to be a society for people whose IQ is at the one-in-a-million level or higher. In point of fact, Mega is a society for people who achieved high enough scores on certain tests -- in my case, the Mega Test. The idea that these tests actually test IQ (whatever that is), and that they have any validity to discern those denizens of such an aethereal realm as one-in-a-million seems laughable to me, as does the behavior of some of the people in Mega. It makes me a little embarrassed to be associa with them, but the Mega Test looked fun (half of it is math), so I took it, got a pretty high score (46 out of 48), and thought I'd check out their lofty Society. I don't claim to be all that smart, however. I know plenty of people smarter than I am. And . . . well, I can't hold a candle to him. >>So no, I will not call you a retard Jim Ferry, as you are not one. Thank you James. Sorry for the melodrama. Sometimes your mathematical ability is so intimidating that I forget there are other ways in which I, perhaps, surpass you, rather than vice versa. It would be difficult to have an equable relationship with someone who exceeds me in every way. >Oh, excuuuuse me for not being as smart as you, James! What happens to me in >the New World Order? Do you send me to the slaughterhouse with all the other >meat animals? >>Huh? Look around you Jim Ferry. There's more than enough slaughter >>going on now to distress the cognizant, and I assure you that I'm not >>doing any of it. >>My efforts to try and prevent some of it, like my emails about Iraq's >>supposed weapons of mass destruction stockpiles, failed. Yes, that's too bad. >>Other efforts of mine have failed as well, and I've learned not to >>carry the world on my shouldenot even in fantasy. As they say, Think globally, act locally. I hope that you don't give up on the world just because you can't save it in one fell swoop. And whatever you do, don't start reading Ayn Rand. Yikes. > Same hint as always: if you don't like it when... > oh, never mind. >>Sigh. I feel a bit guilty now. And I sent you that nasty email >>talking about putting you out of mathematics as well. >>Maybe there IS a problem with how I've gone about things. Yes. Too confrontational. Too alpha male. The hammer (that you use to shape the mathematics forged in your mind) is not the tool to wield in the human realm. > Giggle. Perhaps. Oh tee hee hee yourself. What's your problem, Ullrich? Oh, never mind. >Sure, I've got some trinkets of intellect: M.I.T. degree, some Putnam >medals, Ph.D. from Brown, joined Mega once, mathematician, rocket >scientist, etc. But that's a hell of long way from the serious hardware >that you're interes in: >Abel Prize, Fields Medal, Nobel Prize, Clay Prize, etc. And even the people >who have such hardware aren't necessarily able to follow in your bold footsteps. >So why are you on *my* case? >>Because you *backtracked*!!! Okay, yes! I backtracked! I received a sudden insight, and it just blew me away! I said a lot of crazy things. Now I realize that I'm just not capable of following your intricate logic. So, again, does that make me worthless? I wonder about your moral value system, , where the value of a life is equa solely with its intelligence. A little convenient, no?, that *you* end up valued most this way. >>It would have been better if you'd said nothing at all!!! >>Now I have to toss you into the pile with Barry Mazur, Andrew >>Granville, Ralph McKenzie, David Ullrich, and . >I never claimed to understand your work. Maybe I had a fleeting flash of >intuition that it was correct, but that was all. >>Are you being honest Jim Ferry? >>Please explain to me why you ever claimed my work was correct *in >>detail*. >>I think you owe me that as I'm worried it was some kind of cruel >>prank. Well, I do like a good prank, even if it is cruel, but I don't see how this could be mistaken for one. I mean, I'm the one acting like a fool, right? If someone walks up to you on the street going, flibber jibber jibber and slapping his head while bouncing in circles on one foot, he's not really playing a prank on you. Maybe it's funny (or maybe not), but he's not doing anything *to you*. He's making an ass . . . of himself. I simply had a flash of insight that your work was correct. This jol me out of the ossified mentality of my herdmates. I came to realize that the reasons I *assumed* it was incorrect had to do with cultural assumptions, the same way that I *assumed* Wiles's proof was valid. I star to ponder the implications of your work being correct, and it was frightening. I'd thought I was standing on firm ground. The ground turned to sand, the sand to dust, and the dust scattered in the wind. The world was gone, and there stood to create a new and better world. So yes, I kind of freaked out there. I deified you. But I've calmed down since then. I realized that if I could not turn my flash of insight into a logical chain of reasoning, then it was worthless. I couldn't base anything on it. Your proof is left on equal status with Wiles's: something I can't understand. I felt a little silly. And useless. Then something occurred to me: I was not left in the same place as before. Sure, my mind was not sharpened to the point where I could understand your work, but I *was* at least free of the herd! Free from the outlook of the herd! Free from their incessant mooing! Oh wait, I still read sci.math, so I'm not really free from their incessant mooing. I now have a theory about the meaning behind that initial flash of insight. I believe that I have a purpose: a purpose to help you, James. I can't help you mathematically (and, again, there's no need of that), but I can help you in other ways. With a Plan. In a perfect world, you'd just receive the Plan from the Holy Spirit yourself. But, because of your upbringing perhaps, you can't. So it's up to me. I have been chosen (for some bizarre reason) to receive the Plan. Now I can't receive it perfectly either (I've already pos some pretty foolish things as the Spirit prepared me), nor can you readily accept such a ridiculous thing as the Holy Spirit communicating a plan to someone. Well, maybe you can -- that would make things easier -- but I sort of doubt it. I probably shouldn't have brought up the whole Divine Guidance aspect of this in the first place. Hmmm. > For heaven's sake. Yes, when he says he doesn't understand your > work but thinks it's correct he's joking. For heaven's sake? Interesting choice of words. > Regarding whether it's cruel: I would have never imagined in my > wildest dreams that even _you_ could possibly be so blinded by > megalomania and so desparate for approval that you'd think someone > was being sincere when he says he doesn't understand your > work but nonetheless thinks it's right. I mean that's such an > _utterly_ ridiculous thing to say in a mathematical context that > it's hard to see how anyone could possibly not take it as a joke. > So I'm certain he assumed that you'd realize all along he was > making fun of you. Making fun of you is perhaps a little nasty, > but it's certainly no nastier than you deserve given your obnoxious > nehavior for yeaso it doesn't bother me. > But lately when you start talking like you think he's being sincere > it becomes a whole different story. Actually encouraging a > lunatic's delusions is not a nice thing to do. On the other > hand the fact that you've thought he was sincere is _the_ > most hilarious thing I've ever seen - we need to consider > the greatest good of the greatest number and all that, > being a little nasty to you versus people all over the > planet laughing their asses off, I think it's a wash. > Honest. I point this out just in case you might decide > to try not to be _quite_ so hilarious: People have been > laughing at Jim's parodies for yeabut lately when > you seem to believe he's being sincere, or _might_ > be sincere, in this and rela threads, it really does > add a whole new dimension - goes from hilarious to > absolutely world-class hilarious. Now you know. What baffles me is that I've been one of the particularly sarcastic Harris haters over the years. Why would the Holy Spirit come to me? I'm overwhelmed by the sense of my own unworthiness. But throughout the Bible, especially the New Testament, God is seen to relish working through the biggest sinners. Mary Magdalene. Paul. I'm sorry that the beauty of this was destroyed by your parents. It explains a lot. Interesting that Ullrich is laughing so hard. When one laughs that hard, it's often because he is hiding from a deeper pain. Even were he correct about everything, just why would it be funny? I think maybe David sees something of you in himself, James, which sets up a great deal of conflict. I'd like to tell him to love his own inner Harris but that's just too touchy-feely for my taste. >I was offering a different kind of help. Something to complement and >complete the intense laser of your rational thought. Something to help >bring your theories into the human realm. You don't believe in the efficacy >of such things, I guess, or you just want to sear your way through with that >laser of youso fine. Go get 'em, tiger. You don't need my help. >>Actually I don't need your help, but I *would* appreciate it greatly. >>But how do I know if you're sincere, or just playing some elaborate >>joke? I don't know. The herd seems to think it's a joke too. I guess you just need to evaluate what I say. If I were telling you to go out and kill prostitutes to cleanse the Earth of sin, well, that would be a bad message. But what I'm saying should resonate with a certain part of you yearning for all this bickering to be over. >>As for understanding my work, math proofs begin with a truth and >>proceed by logical steps to a conclusion which then must be true. >>I give you the steps, you follow, and then I'd think you should >>understand. Right. In a perfect world. Have you looked at Wiles's proof? Think how much training that would take to understand. Your requirements are no less demanding, but it's difficult for you to see that. For you, it's easy as pie. -- | Jim Ferry | Center for Simulation | +------------------------------------+ of Advanced Rockets | | http://www.uiuc.edu/ph/www/jferry/ +------------------------+ | jferry@[delete_this]uiuc.edu | University of Illinois | Subject: Re: JSH your ship has come in!!!! >But enough silliness. I don't take orders from James, nor does James give them >at all, as far as I know. At first I didn't realize what my role in all this >was to be, but it's becoming clear to me now. James needs a plan, and for >reasons not clear to me, I have been receiving a plan. It keeps me awake at >night. It distracts me from my work. It is vast and beautiful His plan is not completely vast. About half, I'd say. >Here's to the revolution! I believe in this context, MY role is to be part of the ancien regime. All right then, Ferry, is this to be a call to arms? En garde! If you're not with us, you're against us. I should have suspec you'd side with the upstart, rather than keeping him on the outside of the establishment. And here I thought we could count on you, a compatriot from the Land of Lincoln. Ya just can't trust anyone any more. dave Subject: Talk.Origin banned Subject: Does Mathamitcs prove a Universal designer? A professor of mathematics from the University of Cambridge, P. Dirac, said, in the magazine Scientific American: One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Subject: Re: Talk.Origin banned Subject: Does Mathamitcs prove a Universal designer? > A professor of mathematics from the University of Cambridge, P. Dirac, said, > in the magazine Scientific American: One could perhaps describe the > situation by saying that God is a mathematician of a very high order, and He > used very advanced mathematics in constructing the universe. Generally speaking I find myself in disagreement with Prof. Dirac. It does, I suppose, depend upon exactly what one means by the term advanced mathematics. If one makes the connection that God = laws of nature (physics) the statement that God is a mathematician is basically saying that physics is mathematically based. This makes some sense. However, generally speaking, the more one understands the true basis of these laws the simpler becomes the mathematics. The complexity viewed by man being a result of his improper viewpoint. God as creator, on the other hand, having the central and correct viewpoint defines nature in the most simple of terms and hence used not very advanced mathematics meaning very complex and esoteric, but rather the most simple of mathematics appled to the proper viewpoints and and expanded fractal-like being self-similar at all levels. Just because man has not yet dicovered the proper viewpoint doesn't make God some brain. If I might use the example of the advanced mathematics of planetary motions using epicycles and the greater non-earth centered (simpler) math of sun-centered calculations. In essence the simpler description is in fact more advanced simply because it is simpler, though both may be in a sense correct. Subject: Re: Talk.Origin banned Subject: Does Mathamitcs prove a Universal designer? > A professor of mathematics from the University of Cambridge, P. Dirac, said, > in the magazine Scientific American: One could perhaps describe the > situation by saying that God is a mathematician of a very high order, and He > used very advanced mathematics in constructing the universe. I would have no trouble with that. But what all mathematicians know, and most non-maths people do not know, is that the output of a function will vary with its input. Nor are we dealing with a simple function in a single variable, but a recursive function in almost infinite variables in which you do not get a single output, but a matrix output. Simply put, this accounts for order and randomness. Evolution is easily accommoda within a recursive function of high order. And if random processes are part of the inputs, it is easily seen that the universe is not deterministic. Dirac, btw, was a devout atheist. He may have said what you quo (above) as a general statement, but he did not himself believe in God. In fact, Dirac was so evangelistic about his nonbelief that one of his contemporaries said Dirac has his own religion: 'There is no God, and Dirac is his prophet.' Dirac also said this: The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. This is only natural and to be expec. What however was not expec by the scientific workers of the last century was the particular form that the line of advancement of mathematics would take, namely it was expec that mathematics would get more and more complica, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkehave now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associa with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation. Paper on Magnetic Monopoles (1931) (http://www-gap.dcs.st-and.ac.uk/~history/Quotations/ Dirac.html) Subject: Re: Talk.Origin banned Subject: Does Mathamitcs prove a Universal designer? > A professor of mathematics from the University of Cambridge, P. Dirac, said, > in the magazine Scientific American: One could perhaps describe the > situation by saying that God is a mathematician of a very high order, and He > used very advanced mathematics in constructing the universe. Since Scotty likes to name drop and claims to have met many people, does anyone want to take odds that Scotty has already recently spoken to God about this very point and put God straigth on the matter!. Subject: Re: Talk.Origin banned Subject: Does Mathamitcs prove a Universal designer? > A professor of mathematics from the University of Cambridge, P. Dirac, said, > in the magazine Scientific American: One could perhaps describe the > situation by saying that God is a mathematician of a very high order, and He > used very advanced mathematics in constructing the universe. No, the existence of mathematics does not prove the existence of a Universal designer - in the sense I think you mean it anyway. For example, one possibility is that at the big bang an infinite (or a whole lot) of universes were crea and only those that were internally self consistent survived, in some sense. Or another way of looking at it is that things like arithmetic just must be. 10 apples and 10 oranges must both be dividable into two rows of 5. However, the reverse could well be true. If you believe in God, in some sense he was/is a mathematician. Bill Subject: Another optimization question hi everyone. given a real valued function f that is: 1. defined on a convex set C of $mathbb{R}^n$ (but not defined outside C, we may assume that f is $+infty$ outside of C) and positive (>0) everywhere on C. 2. non-convex in C. 3. continuous and has directional derivatives of all orders for any feasible direction from a point x in C. 4. at each x in C, f(x) can only be compu numerically (has no known closed form). which numerical search algorithms or nonlinear programming techniques would be the best/most effective for finding the local minima and, if possible, a global minimum for this function? any suggestions will be greatly apprecia. thanks in advance. J. Subject: Re: Another optimization question no numerical procedure can reasonably deal with infinity. hence you must use a barrier-approach (adding terms like -log(g_i(x)) for each function g_i which describes a boundary part of C as g_i(x)=0 , with g_i(x)>0 in interior(C), provided such interior exists. otherwise you first must reduce the problem to a subspace where this is the case) . next you could use unconstrained optimization using only function values (e.g. uobyqa from powell or its newer successor, described in a recently published paper in but you must modify this code in order to maintain feasiblitiy, that means you must restrict the possible moves such that feasibility is maintained (via checking the g_i individually). also a grid-search a la torczon comes into mind, again with the moves restric to the feasible part of the grid. hth peter Subject: Re: Quadratic Sieve > Does anyone have or know of a Quadratic sieve implementation that could be > distribu? For Windows, there's an implementation of PPMPQS included with Yuji Kida's UBASIC. I've used it to do composite numbers up to 107 digits. 100-digit composites take about a week with a 2GHz machine. -----= Pos via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- Subject: Re: Quadratic Sieve > For Windows, there's an implementation of PPMPQS included with Yuji Kida's > UBASIC. > I've used it to do composite numbers up to 107 digits. > 100-digit composites take about a week with a 2GHz machine. I'm interes to read that, as it seemed to me that with the standard quadratic sieve (using Montgomery quadratics) there was a limitation on the size of the number one could factorise. I should say that I am not an expert, but gave a course on factorisation a couple of years ago, where I looked at the quadratic sieve as an introduction to the number field sieve. As I explained it, one used quadratics Q(x) = ax^2 + 2bx + c with ac - b^2 = n so that aQ(x) = (ax + b)^2 - n, and one sieved for smooth numbers Q(j) on a sieve centred at the positive root of Q(x). With this method, one has to harvest an even number of smooth numbers from each quadratic (because the factor a^r comes in if there are r factors, and one needs an exact square). But with a sieve size of say 2 million, and a number with 100 digits, one would only get an occasional smooth number from each quadratic and as far as I could see would hardly ever if ever get two. Obviously the algorithm must be modified in some way for numbers this large. Do you know how it was modified? [I haven't looked very carefully through the literature on this -- I'm interes because a student is doing an Msc trying to use the quadratic sieve with parallel processing.] -- Timothy Murphy e-mail: tim /at/ birdsnest.maths.tcd.ie (all email over 80k dispatched to /dev/null) tel: +353-86-2336090, +353-1-2842366 s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland Subject: Re: How much longer must physics put up with F=ma?