mm-1379 === Subject: Sum (k*C(n,k))? Let us assume that the equality S:=SUM_{k=0 to k=n}C(n,k)=2^n is known. If Sigma_1:=SUM_{k=0 to k=n}E(k)=E(0)+E(1)+...+E(n) , then Sigma_2:=SUM_{k=0 to k=n}E(n-k)=E(n)+E(n-1)+...+E(0), that is (1) Sigma_1=Sigma_2 . Further let Sigma_3:=SUM_{k=0 to k=n}k*C(n,k) . According to (1) Sigma_3=SUM_{k=0 to k=n}(n-k)*C(n,n-k)=SUM_{k=0 to k=n}(n-k)*C(n,k), or Sigma_3=n*S-Sigma_3 . In other words Sigma_3=n*S/2 = n*2^{n-1}.Perhaps,help,Alex === Subject: Inconsistent Set Structure ? It follows by construction that if X is consistent, then V[M](X) = 1 (ie, there is a valuation V based on a model M of X where X is true) and for each formula @ e X, V[M](@) = 1 too. But supposed X is inconsistent, does it then follow that V[M](X) = 0 and if @ e X and * e X, then V[M](@) = 0 or 1 and V[M](*) = 0? In other words, while each formula in a consistent set of formulae is true, is it the case that the formulae in an inconsistent set are either all false or some true and some false? And is it the case that if some are true and some are false, then the set of those mixed-value formulae is itself necessarily false too? === Subject: Re: Inconsistent Set Structure ? What is an R-matrix? I am a novice on logic but I do follow it somewhat.I take it that X is a theory , say in first order logic .I thought that a M is a model means V[M] (*)=1 for all *e X (i.e. the formulas of X are all true when the formulas are interpreted as statements about the objects of the model). If X is consistent then It is known that it has a model,that is ,a model M can be constructed for it. If X is inconsistent then there cannot be any model M.Thats supposed to be obvious.So your question does not make sense-there is no model to === Subject: Re: Inconsistent Set Structure ? >What is an R-matrix? I am a novice on logic but I do follow it >somewhat.I take it that X is a theory , say in first order logic. Sorry, X is a set of statements in first-order predicate logic. Since as you say you're a novice, as I am too, perhaps it's best to wait for someone with expertice to give us an answer, but I'll try to clarify. >I thought that a M is a model means V[M] (*)=1 for all *e X (i.e. the >formulas of X are all true when the formulas are interpreted as >statements about the objects of the model). If X is consistent then It >is known that it has a model,that is ,a model M can be constructed for >it. Right. >If X is inconsistent then there cannot be any model M.Thats supposed to >be obvious.So your question does not make sense-there is no model to >calculate truth values. No. Truth values can be calculated for an inconsistent set X, and are expressed as V[M](@) = 0 for some statement @ e X. But I see your point that you'd assume there is no such model, M, so why is there even a valuation? What it means is that from some model M, V(@) = 0. But I wonder if it means for All Possible models M, V(@) = 0. I don't think it has to be that restrictive, but I'm also no logic expert. >What am I missing ? What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose the set of statements @1 through @n entails falsum and thus is inconsistent). Is it the case that for all @ e X, V[M](@) = 0, OR can it be the case that there merely exists at least one @ e X such that V[M](@) = 0? If the latter disjunct, do we also say for X as a whole, V[M](X) = 0? === Subject: Re: Inconsistent Set Structure ? >What is an R-matrix? I am a novice on logic but I do follow it >somewhat.I take it that X is a theory , say in first order logic. > Sorry, X is a set of statements in first-order predicate logic. Since > as you say you're a novice, as I am too, perhaps it's best to wait for > someone with expertice to give us an answer, but I'll try to clarify. >I thought that a M is a model means V[M] (*)=1 for all *e X (i.e. the >formulas of X are all true when the formulas are interpreted as >statements about the objects of the model). If X is consistent then It >is known that it has a model,that is ,a model M can be constructed for >it. > Right. >If X is inconsistent then there cannot be any model M.Thats supposed to >be obvious.So your question does not make sense-there is no model to >calculate truth values. > No. Truth values can be calculated for an inconsistent set X, and are > expressed as V[M](@) = 0 for some statement @ e X. But I see your > point that you'd assume there is no such model, M, so why is there > even a valuation? What it means is that from some model M, V(@) = 0. > But I wonder if it means for All Possible models M, V(@) = 0. I don't > think it has to be that restrictive, but I'm also no logic expert. >What am I missing ? > What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose the set > of statements @1 through @n entails falsum and thus is inconsistent). > Is it the case that for all @ e X, V[M](@) = 0, OR can it be the case > that there merely exists at least one @ e X such that V[M](@) = 0? If > the latter disjunct, do we also say for X as a whole, V[M](X) = 0? Iff X is consistent then there exists at least one iterpretation (candidate model) M such that V[M](@)=1 for all @ in X. Iff X is inconsistent then there is no such M; thus for every interpretation I there is some @ in X such that V[I](@)=0. Clearly, there are interpretations in which some particular consistent @ or consistent subset of @s are true, but there is no interpretation in which all are true. -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: Re: Inconsistent Set Structure ? >> What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose the set >> of statements @1 through @n entails falsum and thus is inconsistent). >> Is it the case that for all @ e X, V[M](@) = 0, OR can it be the case >> that there merely exists at least one @ e X such that V[M](@) = 0? If >> the latter disjunct, do we also say for X as a whole, V[M](X) = 0? >Iff X is consistent then there exists at least one iterpretation (candidate >model) M such that V[M](@)=1 for all @ in X. Iff X is inconsistent then >there is no such M; thus for every interpretation I there is some @ in X >such that V[I](@)=0. Clearly, there are interpretations in which some >particular consistent @ or consistent subset of @s are true, but there is no >interpretation in which all are true. My textbook does not limit valuations within an inconsistent set to a valuation based on the Interpretation V[I](@)=0 as you suggest, but says that for the statement @ in an inconsistent set, V[M](@) = 0, where M is a model wherein V[M](-@) = 1. So the fact that there is no model wherein @ is true does not require omitting the M from notation. And I don't see the necessity for avoiding including the model, M, in the valuation of an inconsistent set member. Having a consistent set Y says there is a model M wherein for all @ e Y, V[M](@) = 1. So having an inconsistent set X says there exists no model, M, wherein V[M](@) = 1, in other words, for all M, V[M](@) = 0. Or not? === Subject: Re: Inconsistent Set Structure ? <81bus0htqta4141eag2e6hvd52lhnir6v0@4ax.com> <3390h9F3uk9b4U1@individual.net> >> What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose the set >> of statements @1 through @n entails falsum and thus is inconsistent). Is it the case that for all @ e X, V[M](@) = 0, OR can it be the case No ,In any choice of interpretation or candidate for a model M, at least one @j is false,that is V[M](@j)=0 (and a possibly different j for each choice of M. >> that there merely exists at least one @ e X such that V[M](@) = 0? If >> the latter disjunct, do we also say for X as a whole, V[M](X) = 0? V[M](X)=0 is shorthand for V[M](@)=0 for every @eX .So ,no you don't have that. >Iff X is consistent then there exists at least one iterpretation (candidate >model) M such that V[M](@)=1 for all @ in X. Iff X is inconsistent then >there is no such M; thus for every interpretation I there is some @ in X >such that V[I](@)=0. Clearly, there are interpretations in which some >particular consistent @ or consistent subset of @s are true, but there is no >interpretation in which all are true. > My textbook does not limit valuations within an inconsistent set to a > valuation based on the Interpretation V[I](@)=0 as you suggest, but > says that for the statement @ in an inconsistent set, V[M](@) = 0, > where M is a model wherein V[M](-@) = 1. So the fact that there is no > model wherein @ is true does not require omitting the M from notation. Could you tell me the name of the textbook you are reading.I might like to read it. > And I don't see the necessity for avoiding including the model, M, in > the valuation of an inconsistent set member. Having a consistent set Y > says there is a model M wherein for all @ e Y, V[M](@) = 1. So having > an inconsistent set X says there exists no model, M, wherein V[M](@) = > 1, in other words, for all M, V[M](@) = 0. Or not? I think you might be misreading .'I' just denotes another candidate for a model or interpretation and is being used instead of the letter M to avoid confusion (but seems to have caused some). Let @ e X (or more generally any statement) .To say @ is inconsistant means the one element set {@} is inconsistent which means not@ is a theorem of first order logic which means V[M](@)=0 for any candidate M.It is only the rest of the statements of your inconsistant set that will be false or true depending on the candidate for the model. Notice also that if s is a statement then s and not_ s might be both consistent (that is ,s is true in some candidates for models (these are models for s) and false in others (these are not models for s).But the set X={s,not_s} is inconsistent and in fact in every candidate for a model (I think interpretation is a better term) esactly one of them is true. I hope this helps.Barbara Knox's reply cleared everything up for me,I think. === Subject: Re: Inconsistent Set Structure ? > What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose > the set of statements @1 through @n entails falsum and thus is > inconsistent). Is it the case that for all @ e X, V[M](@) = 0, > OR can it be the case >No ,In any choice of interpretation or candidate for a model >M, at least one @j is false,that is V[M](@j)=0 (and a possibly >different j for each choice of M. > that there merely exists at least one @ e X such that V[M](@) = 0? > If the latter disjunct, do we also say for X as a whole, V[M](X) = 0? >V[M](X)=0 is shorthand for V[M](@)=0 for every @eX .So ,no you don't >have that. uncertainty. Likewise, V[M](Y) = 1 is shorthand for the case wherein for each @ e Y, V[M](@) = 1. So I was unsure if we'd then be able to say V[M](X) = 0 for the inconsistent set X since (seemingly contrary to such a valuation) X could be inconsistent even if some @ e X were true in some model. Given that we cannot evaluate X, should we then say that the truth value of X is undefined? Also, is it the case that if a set is inconsistent relative to one model that it's also inconsistent relative to *any* model? I tend to think that might be the case. >>Iff X is consistent then there exists at least one iterpretation >(candidate >>model) M such that V[M](@)=1 for all @ in X. Iff X is inconsistent >then >>there is no such M; thus for every interpretation I there is some @ >in X >>such that V[I](@)=0. Clearly, there are interpretations in which >some >>particular consistent @ or consistent subset of @s are true, but >there is no >>interpretation in which all are true. >> My textbook does not limit valuations within an inconsistent set to >> valuation based on the Interpretation V[I](@)=0 as you suggest, but >> says that for the statement @ in an inconsistent set, V[M](@) = 0, >> where M is a model wherein V[M](-@) = 1. So the fact that there is no >> model wherein @ is true does not require omitting the M from >notation. >Could you tell me the name of the textbook you are reading.I might >like to read it. http://www.amazon.com/gp/reader/0226280853/ref=sib_dp_pt/102-2981968-0288141 What I cite is from page 151. Believe me, you will like to read this book! It's far and away the best logic text I have ever read. >> And I don't see the necessity for avoiding including the model, M, >> the valuation of an inconsistent set member. Having a consistent set >> says there is a model M wherein for all @ e Y, V[M](@) = 1. So having >> an inconsistent set X says there exists no model, M, wherein V[M](@) >> 1, in other words, for all M, V[M](@) = 0. Or not? >I think you might be misreading .'I' just denotes another candidate >for a model or interpretation and is being used instead of the letter M >to avoid confusion (but seems to have caused some). Maybe I am misreading, but I read Barbara as saying one should NOT use M, while my text does use M in the valuation V[M](@) = 1 where @ is a member of an inconsistent set. But your response above addresses my question after which this is I or M issue somewhat of an aside, but interesting nonetheless since I'd not seen 'I' for the interpretation function used in valuation notation before, is it a standard? >inconsistant means the one element set {@} is inconsistent which means >not@ is a theorem of first order logic which means V[M](@)=0 for any >candidate M.It is only the rest of the statements of your inconsistant >set that will be false or true depending on the candidate for the >model. Right, right. Well said. >Notice also that if s is a statement then s and not_ s might be >both consistent (that is ,s is true in some candidates for models >(these are models for s) and false in others (these are not models for >s).But the set X={s,not_s} is inconsistent and in fact in every >candidate for a model (I think interpretation is a better term) esactly >one of them is true. So if for all @ e X, V[M](@) = 0, then V[M](X) = 0 too... right? === Subject: Re: Inconsistent Set Structure ? [SNIP] > Also, is it the case that if a set is inconsistent relative to one > model that it's also inconsistent relative to *any* model? I tend to > think that might be the case. A set of statements X is inconsistent iff there is NO interpretation that evaluates all the statements of X as true. So inconsistency is with respect to ALL possible interpretations, not just some particular one. And certainly for any consistent non-empty set of statements X there will be SOME interpretations that evaluate some or all of the statements to 0, but that doesn't make X inconsistent -- you only need ONE all-true interpretation (i.e. a model) to show that X is consistent. For example, the set of statements X consisting of the single statement P() (a predicate of no arguments) has exactly 2 interpretations for any domain, one of which has P() being true and the other false. Since there is some interpretation where all of X evaluates to true, X is consistent. -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: Re: Inconsistent Set Structure ? >[SNIP] >> Also, is it the case that if a set is inconsistent relative to one >> model that it's also inconsistent relative to *any* model? I tend to >> think that might be the case. >A set of statements X is inconsistent iff there is NO interpretation that >evaluates all the statements of X as true. So inconsistency is with respect >to ALL possible interpretations, not just some particular one. >And certainly for any consistent non-empty set of statements X there will be >SOME interpretations that evaluate some or all of the statements to 0, (Oops: if the statements are all universally valid (e.g. tautologies) then no interpretation can evaluate any of them to 0.) >but that doesn't make X inconsistent -- you only need ONE all-true >interpretation (i.e. a model) to show that X is consistent. >For example, the set of statements X consisting of the single statement >P() (a predicate of no arguments) has exactly 2 interpretations for any >domain, one of which has P() being true and the other false. Since there is >some interpretation where all of X evaluates to true, X is consistent. -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: Re: Inconsistent Set Structure ? >>I think you might be misreading .'I' just denotes another candidate >>for a model or interpretation and is being used instead of the letter M >>to avoid confusion (but seems to have caused some). > Maybe I am misreading, but I read Barbara as saying one should NOT >use M, while my text does use M in the valuation V[M](@) = 1 D'oh! Sorry... my text does use M in the valuation V[M](@) = 0 >where @ >is a member of an inconsistent set. But your response above addresses >my question after which this is I or M issue somewhat of an aside, but >interesting nonetheless since I'd not seen 'I' for the interpretation >function used in valuation notation before, is it a standard? === Subject: Re: Inconsistent Set Structure ? > What I'm asking is, suppose @1, ..., @n |- _|_ (ie, suppose the set > of statements @1 through @n entails falsum and thus is inconsistent). > Is it the case that for all @ e X, V[M](@) = 0, OR can it be the case > that there merely exists at least one @ e X such that V[M](@) = 0? If > the latter disjunct, do we also say for X as a whole, V[M](X) = 0? >>Iff X is consistent then there exists at least one iterpretation (candidate >>model) M such that V[M](@)=1 for all @ in X. Iff X is inconsistent then >>there is no such M; thus for every interpretation I there is some @ in X >>such that V[I](@)=0. Clearly, there are interpretations in which some >>particular consistent @ or consistent subset of @s are true, but there is no >>interpretation in which all are true. > My textbook does not limit valuations within an inconsistent set to a >valuation based on the Interpretation V[I](@)=0 as you suggest, but >says that for the statement @ in an inconsistent set, V[M](@) = 0, >where M is a model wherein V[M](-@) = 1. So the fact that there is no >model wherein @ is true does not require omitting the M from notation. > And I don't see the necessity for avoiding including the model, M, in >the valuation of an inconsistent set member. Having a consistent set Y >says there is a model M wherein for all @ e Y, V[M](@) = 1. So having >an inconsistent set X says there exists no model, M, wherein V[M](@) = >1, in other words, for all M, V[M](@) = 0. Or not? Another way to look at it (warning: novice winging it), if S is a set of statements in first-order predicate logic and S is consistent, then (x)((x e S) -> (Ix e M)) ie, for all x, if x is in S, then the Interpritation of x (Ix) is in the model M. So if on the other hand set S is not consistent, then -(x)((x e S) -> (Ix e M)) ie, it is not the case that for all x, if x is in S, then the Interpritation of x (Ix) is in the model M, and thus (Ex)((x e S) & -(Ix e M)) ie, there exists some x in S the Interpretation of which (Ix) is not in the model M. That's different than the way I expressed it above, and it's not against saying V[I](@)=0, but as far as I can see it's also not against the notation V[M](@)=0. And it would seem to me that so long as we have an interpretation function I, we assume as its range some model M into which I maps (or fails to map) any given member @ of S onto I(@) in M; so if we say there is an I function, then we also say there is an M, whether or not I(@) resides in M. No? === Subject: Unified Theory Using Damped Oscillation - (In Comparison To) - The Smart Universal Model Unified Theory Using Damped Oscillation - (In Comparison To) - The Smart Universal Model -------------------------------------------------------------------------- --------------------------------- Unified Theory Using Damped Oscillation http://www3.sympatico.ca/georg.josephs/index.htm http://www3.sympatico.ca/georg.josephs/Part21.htm#_1_17 Quote from above reference LINK: -------------------------------------------------------------------------- ------------------------ Compression of Three Smart Equations into One D.O.T. Equation -------------------------------------------------------------------------- ------------------------ Given: Equations on Smart1234 website. L*Q'' + RQ' +[1/C]Q=0 Q'' +[R/L] Q' + [1/(LC)] Q = 0 (R/L)=> 1/(31/2p)=> 0.1837 1)l=656 nm R/L=0.2/12.1 =0.0165289y(5/3)(1/100)=B1 2) l=486 nm R/L=0.2/(3.954)=0.0505817y(10/2)(1/100)=B2 3) l=433 nm R/L =0.2/7.986=0.02510y(5/2)(1/100)=B3 And: (5/3)+(5/1)+(5/2)=9.1667 =B1+B2+B3 And: 2*9.1667=18.3334 y1/(31/2p)*100 =>2b =>2B in D.O.T. As in: U''+B*U'+k*U=0 B=1/(31/2p)=[mp+mn]/me*(ü) y0.1837.0=1836+1=proton+electron Therefore, the combined equation is: U''+[1/(31/2p)]U'+k*U=0 The tripartite nature of the equation is exemplified by: 1/(31/2p)=> 31/2=> 3rd Fresnel zone For: 1/(31/2p)=cos(w) w=79.41 degrees For He, ground state, p. 387, Alberty, we have: E=79.0 eV => 79.41 degrees For the H-atom: 50*31/2/32= sec(w) 2.7063=sec(w)=> H-atom => Eh=Hartree=27.211608 eV Eh/2=13.605 eV (2.7063/2)=1.35315 For the He-atom=2*(H-atom) 100*31/2/32=sec(w)=5.4127 => 54.5 eV => 2nd Ionization Energy w=79.35 degrees => 79.0 eV ground state, p. 386, Alberty. For the Li-atom: 20=18+2=[core=protons]+[2 electrons] 20*31/2/32=sec(w) w=(180+22.5) degrees =202.5 degrees w=22.5 degrees ground state=-203.48 eV => 202.5 degrees For the H-atom: 19*31/2/32=sec(w) w=13.4876yEh/2 (18+1)=19=[H-atom core=proton]+[1 electron] For Li: Li=3*H=3*50*31/2/32=sec(w) 150*31/2/32=> w=82.9 degrees 100-17=83 =>20 Therefore, for the new, proposed, secant equation, we can infer the following correlations. Equation: N*31/2/32=sec(w) N=19=>H N=20=>Li N=21=> B N=100=> He N=200=> Be The validity of this equation will be tested in future parts and sections. vs. The Smart Universal Model http://members.aol.com/smart1234/SmartPage1.htm It appears Georg Werner Josephs has done some very interesting work with the D.O.T. Theory . The Smart Model is basically in agreement with the DOT Theory. You can even see from the reference LINK, how the Smart Model does fit in, into a Unified Universal Field which can apply to all levels of the universe. I'm happy to see Georg Werner Josephs even used some of my work as a reference in the development of The DOT Theory. He even shows that the elements are made of particular intelligent structures. The Smart Model also has shown this. It appears there are intelligent people out there that can see that the universe can be unified using a particular type field. The DOT Theory using the damped oscillation approach to unifing the universe. The Smart Model does this too except there is a few slight differences. The Smart Model uses the damped oscillation approach too ((Externally)) with respect HELIX SPIRAL SPINNING FIELDS. But the Smart Universal Model shows the Internal Structure Field as well. The Smart Universal Model not only unifies the external field with the internal field, but even goes to the areas that determines where inanimate matter and energy begins-end to the point where animate matter begins and ends. It also shows perpetual motion, in conflict with entropy and where eventually perpetual motion will finally be reached in a Unified Universal State of Perfection. The diagram below basically shows how The Smart Model Universe is related to The DOT Model Universe. ( Internal) The Smart Universal Model is here. | | | External v v v External (((( ( (< -- ( HELIX SPIRAL SPINNING FIELDS) --->) ) ))))) ^ ^ |_____________________________________________| | The DOT Universal Model starts here. The DOT Universal Model is located where the external damped oscillations occur throughout the universe from the micro-atomic level to the macro-universal level. My compliments for The DOT Theory. Very Good! - Smart1234 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Smart1234 Challenges the Accuracy of Pi itself... . Smart1234 Challenges the Accuracy of Pi itself... . Let's see Standard Analysis has found pi = 3.14159... . But I think it may be something else. The Smart Model Pi phi = 1/2 ( 1 + sqrt (5) ) = the Golden Ratio = The Divine Proportion phi = 1.6180339887... 1/phi = smallest radius for covering the circle area of 5 symmetrical disks with a common origin for a unit disk = 1 A / r^2 = Smart Model Pi = Pi_sm 1/[1/(1/2(1 + sqrt(5))]^2 = Pi_sm 2.6180339887498... = Pi_sm http://mathworld.wolfram.com/DiskCoveringProblem.html http://mathworld.wolfram.com/FiveDisksProblem.html http://mathworld.wolfram.com/FibonacciNumber.html http://mathworld.wolfram.com/GoldenRatio.html http://mathworld.wolfram.com/Pentagram.html http://mathworld.wolfram.com/GoldenTriangle.html http://mathworld.wolfram.com/Dodecagon.html http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . You know, people don't like it when you say pi is what it ain't! http://www.cecm.sfu.ca/projects/ISC/data/pi.html pi to several digits. Poly-poly man === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . >You know, people don't like it when you say pi is what it ain't! >http://www.cecm.sfu.ca/projects/ISC/data/pi.html >pi to several digits. >Poly-poly man Nature likes me. I'm sorry if people don't. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . You haven't proved anything. You've just repeated that you want pi to be related to phi. === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . Or, (sorry if I'm contradicting myself) but in the false proofs thread, there is quite a proof: Take a semicircle of radius 1. Its length is pi. Divide the diameter in n equal parts and with each one of them as diameter, draw a semicircle. The length of all of them small semicircles is n*pi*(1/n) = pi with independence of n. Take the limit as n go to infinity. All the semicircles, with whole constant length of pi, tend to the diameter of the initial semicircle, that We were both wrong. Best Wishes, Poly-Poly Man === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . > You know, people don't like it when you say pi is what it ain't! > http://www.cecm.sfu.ca/projects/ISC/data/pi.html > pi to several digits. > Poly-poly man That is only the first 50,000,000 digits of pi, where can I find the rest? === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . In sci.math, S. Enterprize Company > Smart1234 Challenges the Accuracy of Pi itself... . > Let's see Standard Analysis has found pi = 3.14159... . > But I think it may be something else. [rest snipped] You'll have to get in line behind the religious fruitcakes; they've already entered a petition on redefining it to be exactly 3. I think at this point it's tied up in committee. -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . >Smart1234 Challenges the Accuracy of Pi itself... . >Let's see Standard Analysis has found pi = 3.14159... . > But I think it may be something else. >The Smart Model Pi >phi = 1/2 ( 1 + sqrt (5) ) = the Golden Ratio = The Divine Proportion >phi = 1.6180339887... >1/phi = smallest radius for covering the circle area of 5 symmetrical disks >with a common origin for a unit disk = 1 >A / r^2 = Smart Model Pi = Pi_sm >1/[1/(1/2(1 + sqrt(5))]^2 = Pi_sm >2.6180339887498... = Pi_sm >http://mathworld.wolfram.com/DiskCoveringProblem.html >http://mathworld.wolfram.com/FiveDisksProblem.html >http://mathworld.wolfram.com/FibonacciNumber.html >http://mathworld.wolfram.com/GoldenRatio.html >http://mathworld.wolfram.com/Pentagram.html >http://mathworld.wolfram.com/GoldenTriangle.html >http://mathworld.wolfram.com/Dodecagon.html >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html Another reference LINK http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . >>Smart1234 Challenges the Accuracy of Pi itself... . >>Let's see Standard Analysis has found pi = 3.14159... . >> But I think it may be something else. >>The Smart Model Pi >>phi = 1/2 ( 1 + sqrt (5) ) = the Golden Ratio = The Divine Proportion >>phi = 1.6180339887... >>1/phi = smallest radius for covering the circle area of 5 symmetrical disks >>with a common origin for a unit disk = 1 >>A / r^2 = Smart Model Pi = Pi_sm >>1/[1/(1/2(1 + sqrt(5))]^2 = Pi_sm >>2.6180339887498... = Pi_sm >>http://mathworld.wolfram.com/DiskCoveringProblem.html >>http://mathworld.wolfram.com/FiveDisksProblem.html >>http://mathworld.wolfram.com/FibonacciNumber.html >>http://mathworld.wolfram.com/GoldenRatio.html >>http://mathworld.wolfram.com/Pentagram.html >>http://mathworld.wolfram.com/GoldenTriangle.html >>http://mathworld.wolfram.com/Dodecagon.html >>http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html >Another reference LINK >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits (Another reference LINK Read section Why does phi appear in nature? They show a clearer breakdown of the 360 degrees in a circle and nature patterns similarities of the circle...) http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . >A / r^2 = Smart Model Pi = Pi_sm >1/[1/(1/2(1 + sqrt(5))]^2 = Pi_sm Why do you claim that A=1? === Subject: Re: Smart1234 Challenges the Accuracy of Pi itself... . >>A / r^2 = Smart Model Pi = Pi_sm >>1/[1/(1/2(1 + sqrt(5))]^2 = Pi_sm >Why do you claim that A=1? By definition, of a Unit Disk with the smallest possible radius under the conditions shown which relates pi to a spiral using the Golden ratio. The form of the Golden ratio in nested radical form is, phi = sqrt(1 +sqrt(1+sqrt1 + .... sqrt(1)) The form of pi in nest form is, pi = lim 2^n+1 = sqrt(2+sqrt(2+sqrt(2+...+sqrt(2)) Phi in the form of a continued fraction is, Phi = 1 + 1 ------------ 1 + 1 -------- 1 + 1 ------ 1+ ... Phi also has this form, Phi = 1/2 ( 1 + sqrt(5)) = 1.6180339... Phi and Pi have almost identical patterns in wave form analysis, except pi uses sqrt(2) in it's patterns and Phi used sqrt(1) in it's patterns. For a Unit Circle, Unit Circle = 1 The Smart Model Pi is closer related to unity or 1. In the 5 disk problem, the smallest radius that can be formed for a Unit Disk is, 1/Phi = .6180... In the Disk Covering Problem, they use the area that fills in this smallest circle with a symmetrical pattern of circles with a common origin with the smallest circle radius. References http://mathworld.wolfram.com/DiskCoveringProblem.html http://mathworld.wolfram.com/FiveDisksProblem.html I think one of the main difference between Phi and pi is, Phi uses the sqrt(1). Pi uses the sqrt(2). Which looks more accurate? sqrt(1) = 1 or sqrt(2) = 1.41421... The sqrt(1) look more accurate to me for a NEW definition of pi. Phi and Pi almost sound the same. They are very closely related. I think Phi is more accurate in relation to the Fibonacci Spiral. It also uses the Golden Ration. I'm not saying pi doesn't work for something used in the calculating of circles anf spheres, but Pi_sm seems to me to be more accurate in it's relation to a spiral. A good analogous example of Pi_sm is like looking a a CD. The groves look like a circle but if you look closer it's like a very fine compact spiral that forms a circle. If you go to the limits of infinity, this circular spiral looks just like a circle on it's outer edge. With a more precise form of pi, I think more accurate values can be found in nature relative to Pi_sm. Where, Pi_sm = Smart Model Pi The Smart Model uses basically the Helix Spiral Field in it foundations of calculations in the process of Unifing the universe at all levels of analysis from micro to macro. Who appears to be more accurate in nature and life? In nature things appear in spiral form like for example plants and flowers, and even you. You hand itself is related to the Golden Ratio which has the pattern, 1, 3, 5.. You have one hand, 5 fingers, 3 spaces separating the fingers by knuckles etc... . Even the iris of your eye isn't a circle but something similar to a (CD-spiral) with a center hole. So in my opinion, Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: The state-of-the-art in mathematics by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBPEwFl30146; >> The point I really wanted to convey is that whenever a concept is >> ill-defined it is bound to lead to contradiction. The origin of i is >> the equation x^2 + 1 = 0. i is supposed to be the solution of this >> equation among the real numbers which does not exist. >Bullshit (as usual). i is an element adjoined to the reals to extend the >real field to a field wherein the irreduciable equation x^2 + 1 = 0 has >a root. i is NOT a real number and the complex field contains the real >field properly and a subfield. The number i is no more mysterious than >adjoining the square root of 2 to the rational field to get an extension >wherein the equation x^2 - 2 = 0 has a solution. >Google . Shmuck! >Has anyone ever told you that you are a troll and a mathematical >incompetent? No? Well I am telling you now. >Bob Kolker Extending a mathematical space, including the adjoining of any mathematical object, does not well-define that larger space. It needs a its own set of axioms to well-define it. In this case you need to well-define the complex field. In general an irrational number is notg well-defined unless every digit is known or computable from the axioms of the real number system. In some of my threads here I pointed out that the real number system is ill-defined because two of its axioms - the trichotomy and completeness axioms - are false. Counterexamples to them were constructed by Brouwer and Banach-Tarski, respectively. References are cited. Your name-calling can never substitute for your ignorance. You might learn from the experience of Ullrich and Israel. I'll prove your ignorance with this simple request: well-define a real number. If you can answer this question correctly I'll send a check for $1,000. If you can't you owe me $1,000. It must be different from my development of the new real number system. E. E. Escultura University of the Philippines === Subject: Re: The state-of-the-art in mathematics > Extending a mathematical space, including the adjoining of any > mathematical object, does not well-define that larger space. The grinding sound we hear is that of a Crank turning. Bob Kolker === Subject: Re: The state-of-the-art in mathematics by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBPEwFO30152; > > The point I really wanted to convey is that whenever a concept is > ill-defined it is bound to lead to contradiction. The origin of i is > the equation x^2 + 1 = 0. i is supposed to be the solution of this > equation among the real numbers which does not exist. >>Bullshit (as usual). i is an element adjoined to the reals to extend the >>real field to a field wherein the irreduciable equation x^2 + 1 = 0 has >>a root. i is NOT a real number and the complex field contains the real >>field properly and a subfield. The number i is no more mysterious than >>adjoining the square root of 2 to the rational field to get an extension >>wherein the equation x^2 - 2 = 0 has a solution. >>Google . Shmuck! >>Has anyone ever told you that you are a troll and a mathematical >>incompetent? No? Well I am telling you now. >>Bob Kolker > Don't pay much attention to this, he tells everyone this that he doesn't >agree with in math. . >Smart's Alt. Physics News Group >ht tp://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >S. Enterprize (Science Journal) >http://smart1234.s-enterprize.com / Yes, two others in his small circle have already fallen into a pit. He is on the verge of it in another thread. E. E. Escultura University of the Philippines === Subject: Has anyone sent a gift to Father Christmas? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBPEwFw30141; PLease help me with this very difficult problem... A parisher, Alain. === Subject: Re: Prime? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBPEwGJ30173; >So what definition are you using for prime and composite anyway? A prime is an integer >1 that cannot be divided with a zero remainder by any other integer other than itself and 1. A composite is an integer >1 that can be divided with a zero remainder by itself and 1 and other primes. Dan === Subject: Re: Prime? Multiplying a natural number by a prime is like adding a brick to a wall--the wall gets greater, the number gets multiplicatively greater. Multiplying by 1 does nothing, is nothing-- the multiplied number stays the same. 1 is no multiplicative brick, it's not a prime, it's just nothing (multiplicatively). Number 1 is not a composite either since it is not a product of two numbers which are multiplicatively something (any natural number different from 1 is something). On the other hand, number 0 in the domain of integers or in the domain of non-negative integers is composite. Indeed, 0 is not nothing multiplicatively -- multiplying by 0 changes the multiplied numbers, e.g. 0*1=0, 0*2=0 etc (to be something it is enough to affect even one number, but never mind). Moreover, 0 is a product of two numbers where BOTH are something, for instance 0=0*0, 0 = 0*2, 0=0*999 (but equality 0=0*1 proves nothing, since 0 is nothing). Su8mmary: Number 1 is not a prime. Number 1 is not composite. Number 1 is multiplicatively nothing. Number 0 is not a prime. Number 0 IS composite. Nember 0 is multiplicatively something. (One may say that multiplicatively 1 is what additively is 0; additively 1 is the only prime in the additive semigroup of natural numbers; and in the additive monoid of non-negative integers). -- Wlod === Subject: Re: Prime? In general, when we go beyond the multiplicative monoid o natural numbers, it may happen that product of two elements give multiplicatively nothing, i.e. a*b = 1 Then, multiplicatively, a b are nothing. Formally, they are called units. An element e can be THE unit -- that's when e*x = x for every x; or it can be A unit, when e*f is THE unit for a certain element f (then f is the inverse of e, and e is the inverse of f). All this is formalized in the framework of commutative monoids (for general, not necessarily commutative, monoids the situation is a bit more complex). Monoid is a set M together with an element 1, and with an associative operation *, for which 1 is the unit element. To speak easily about primes etc it's more comfortable to restrict one's attention to commutative operations * only. ****** It's possible to consider just commutative semigroups, where a semigroup is a set S together with an associative operation *. Element u of S is a unit (nothing), when every element is divisible by u, i.e. for every x in S there should be y in S such that x = y*u. And the rest is the same, except that there is no need to mention THE unit -- possibly there is none. But if there is A unit, then there is also THE unit. (The unit is unique). -- Wlod **** === Subject: speed of light inside a carbon atom is 1 x10^8 m/s and not 3 x 10^8 m/s Re: plugging in Permeability in Schrodinger Equation to solve for speed of light Perhaps the other way maybe easier. If we make a list of the inside structure of all the elements of the Periodic Table starting with hydrogen as to number of subshells inside of shells for pi and e value then for hydrogen and helium the pi and e value would be 1 subshell inside of 1 shell and so pi and e value for such a Universe of a Hydrogen or Helium Atom Totality would be 1/1 and 1/1 or 1. So if human life lived inside a Hydrogen or Helium Atom Totality then they would discover pi with a value of 1 and e with a value of 1 in their Universe. For a Carbon Atom Totality there are 3 subshells inside of 2 shells and human life in that universe would find pi to have a value of 3/2 or 1.5 and e would also be 1.5. In a Plutonium Atom Totality, human life discovers pi as 22/7 and e as 19/7 for values not in irrational number form but rational number form of 3.14 and 2.71. So the inside structure of atoms of the Periodic Table give a value of pi and e ranging from 1 to that of 3.14 (not counting the transplutonium atoms) Now, using the Schrodinger Equation we can compile what a radius for the elements are and they range from approx 0.5 to 2.5 x 10^-10 meters And so the distance measure radii somewhat closely resembles the variation in pi. Now Force such as Coulomb Force is the inverse square which is geometrically a area and the surface area of Riemannian geometry such as a cylinder or sphere or lobe. And the speed is the square root of inverse factors. So now, in broad general terms, if the inside structure of all the atoms of the Periodic Table vary in distance from about 1 to 3 then the Coulomb Force for all the elements of the Periodic Table range from 1^2 to that of 3^2 or have a variance of anywhere from 1 to 9. And in broad general terms the speed of light inside the atoms of the Periodic Table would then have a variance of sqrt 1 to sqrt 9 or 1 to 3. Thus or therefore, we should find that the SPEED OF LIGHT inside a fluorine atom is approximately 1 x 10^8 m/s whereas the speed of light inside a plutonium atom with its 5f6 has a value of 3 x 10^8 m/s. If our Universe were a Carbon Atom Totality then our mathematics textbooks would all be saying that the value of pi and e is 1.5 and the value for the speed of light in this universe is measured as 1 x 10^8 m/s. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Special Relativity breaks-down inside of atoms where c varies Re: speed of light inside a carbon atom is 1 x10^8 m/s and not 3 x 10^8 m/s Re: plugging in Permeability in Schrodinger Equation to solve for speed of light > So now, in broad general terms, if the inside structure of all the atoms of > the Periodic Table vary in distance from about 1 to 3 then the Coulomb > Force for all the elements of the Periodic Table range from 1^2 to that of > 3^2 or have a variance of anywhere from 1 to 9. And in broad general terms > the speed of light inside the atoms of the Periodic Table would then have a > variance of sqrt 1 to sqrt 9 or 1 to 3. > Thus or therefore, we should find that the SPEED OF LIGHT inside a fluorine > atom is approximately 1 x 10^8 m/s whereas the speed of light inside a > plutonium atom with its 5f6 has a value of 3 x 10^8 m/s. > If our Universe were a Carbon Atom Totality then our mathematics textbooks > would all be saying that the value of pi and e is 1.5 and the value for the > speed of light in this universe is measured as 1 x 10^8 m/s. Obviously then the speed of light is a constant in Special Relativity only to that particular inside structure of that particular chemical element. Since the Cosmos is inside a big atom of 231Pu then the speed of light is a constant 3 x 10^8 m/s. And so we can have Special Relativity on a cosmic scale because it is the inside of a particular atom. But when we measure the speed of light inside of a hydrogen atom or helium atom or carbon atom or gold atom or lead atom then the speed of light inside those atoms is not 3 x 10^8 m/s but varies from 1 x 10^8 m/s to 3 x 10^8 m/s because the value of pi and e inside those atoms varies from 1 to 3.14... So Special Relativity is a law of physics but confined to only the cosmos and not the inside of atoms within the cosmos. Because the speed of light is not a universal constant, just as the value of pi and e are not universal constant values but vary depending on where you measure. If my above is not true, then what must happen is that either the Coulomb force is false and needs changing or else Special Relativity is false and needs changing. Most everyone who knows enough science would stick with Coulomb force and Maxwell Equations and happy to change and modify Special Relativity. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: Special Relativity breaks-down inside of atoms where c varies Re: speed of light inside a carbon atom is 1 x10^8 m/s and not 3 x 10^8 m/s Re: plugging in Permeability in Schrodinger Equation to solve for speed of light Nothing. I cannot believe how incredibly stupid Archie-Poo is. I mean rock-hard stupid. Blazing hot mid-day sun on Mercury stupid. Surface of Venus under 80 atmospheres of red hot carbon dioxide and sulfuric acid vapor dehydrated for 300 million years rock-hard stupid. Stupid so stupid that it goes way beyond the stupid we know into a whole different sensorium of stupid. Archie-Poo is trans-stupid stupid. Meta-stupid. Stupid so collapsed upon itself that it is within its own Schwarzschild radius. Black hole stupid. Stupid gotten so dense and massive that no intellect can escape. Singularity stupid. Archie-Poo emits more stupid/second than our entire galaxy otherwise emits stupid/year. Quasar stupid. Nothing else in the universe can be this stupid. Archie-Poo is an oozingly putrescent primordial fragment from the original Big Bang of Stupid, a pure essence of stupid so uncontaminated by anything else as to be beyond the laws of physics that define maximally extrapolated hypergeometric n-dimensional backgroundless stupid as we can imagine it. Archie-Poo is Planck stupid, a quantum foam of stupid, a vacuum decay of stupid, a grand unified theory of stupid. Archie-Poo is the epiphany of stupid. Archie-poo is stooopid. Archie-Poo is a swine. Archie-Poo is a vulgar little maggot. Archie-Poo is a worthless bag of filth. As they say in Texas, Archie-Poo couldn't pour piss out of a boot with instructions printed on the heel. Archie-Poo is a canker, an ulcerous sore that won't go away. I would rather watch Affirmative Action lawyers suck-start Harleys with their bungholes than suffer the troll abominations of Archie-Poo. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: experiments to show the variability Re: Special Relativity breaks-down inside of atoms where c varies > If my above is not true, then what must happen is that either the Coulomb > force is false and needs changing or else Special Relativity is false and > needs changing. Most everyone who knows enough science would stick with > Coulomb force and Maxwell Equations and happy to change and modify Special > Relativity. And we all at some time must grapple with the question as to why we would think that Special Relativity is not quantized. Why would the Maxwell Equations be not quantized. Would any of us take Special Relativity as a higher truth than the Maxwell theory? I should think not. The way the Maxwell Equations are quantized is that the speed of light is caused by the Permittivity and Permeability which are electric factor and magnetic factor just as a light wave is a transverse wave of electric and magnetic. And so inside each element from hydrogen to helium to carbon to lead to curium, all have a quantized permittivity and permeability depending on their internal structure and each has a different permeability. A quantized permeability. And the speed of light is a constant inside each one of these chemical elements but they vary in value from 1 x 10^8 m/s to 3 x 10^8 m/s. Just as they vary in radius from about 0.5 x 10^-10 m to 2.5 x 10^-10 m. And just as they vary in geometrical shape as well as subshells in shells. Maxwell theory holds true everywhere, but Special Relativity holds true only inside a specific chemical element. And it happens that our cosmos is the inside of a plutonium atom where pi is 22subhells/ 7 shells and where e is 19 subshells occupied/ 7 shells and where the permittivity and permeability constants make for a speed of light of 3 x 10^8 m/s. If we were humans inside of a Hydrogen or Helium Atom Totality our math texts will measure pi at a value of approx 1 and our value for e is also approx 1 because there are 1 subshell/1 shell. And our physics texts in such a cosmos will measure the speed of light at approx 1 x 10^8 m/s and a speed of 3 x 10^8 m/s would be an impossible speed inside of hydrogen and helium. Which raises an interesting question which my mind is now grappling with. How can I prove the above by an experiment, a deciding experiment. All I have is the logic that the above must be true to hold consistency. We cannot have Special Relativity and Maxwell Equations and one speed of light constant. There is a contradiction in those. So what must fall is Special Relativity because the speed of light must have a different constant inside of each chemical element. So how can I prove it with a Deciding Experiment? That maybe a tough one. So let me give it some thought. I do know that light is slowed down when traversing a denser material such as say diamonds. But can there be a discrepancy or difference measured from 1 to 3 x 10^8 m/s. Which seems like a small difference that the equipment needs to be extra sensitive. Then there are the radioactive glowing elements such as radium. Has anyone attempted to measure the speed of radioactive-light as to whether it is 3 x 10^8 m/s or whether it seems to be a sluggish and slower speed. So I am looking for experimental situations in which light is emitted from the inside of atoms and appears to be more slow or sluggish than expected. P.S. if we keep the Permittivity a constant inside atoms then the Permeability varies to create that variance in light speed. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: experiments to show the variability Re: Special Relativity breaks-down inside of atoms where c varies > I do know that light is slowed down when traversing a denser material such as say > diamonds. But can there be a discrepancy or difference measured from 1 to 3 x > 10^8 m/s. Which seems like a small difference that the equipment needs to be > extra sensitive. Then there are the radioactive glowing elements such as radium. > Has anyone attempted to measure the speed of radioactive-light as to whether it > is 3 x 10^8 m/s or whether it seems to be a sluggish and slower speed. So I am > looking for experimental situations in which light is emitted from the inside of > atoms and appears to be more slow or sluggish than expected. > P.S. if we keep the Permittivity a constant inside atoms then the Permeability > varies to create that variance in light speed. Now I wonder if the speed of light slowing down in diamonds is a result of the light being captured by the carbon atoms and then re-emitted but at a slower speed. Taking a look at the radii of carbon to silicon is that the silicon is about twice the radii of carbon. So guess estimating that the speed of light inside carbon is about 1 x 10^8 m/s and in silicon is about 2 x 10^8 m/s or twice as fast in glass re-emission than in diamond re-emission. I never really was fully satisfied in physics explanations that speed of light slows down in denser mediums yet on the other hand have Special Relativity dictate that c is a constant. Seems like those two heads of a snake were enjoined in a contradiction. But if a reflector such as diamond or glass absorbed the photon and then re-emitted the photon that the speed of the re-emission would be what the speed of light inside that material is, which varies from chemical elements. Then again the density explanation may be all true and the varying speed of light inside of atoms is an extra new factor on top of density to consider. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: experiments to show the variability Re: Special Relativity breaks-down inside of atoms where c varies Archie, If Uncle Al did not take off time to slate you now and again, you would be conducting a monologue with yourself. Are you managing to teach yourself something, or are you too stupid for that? Franz === Subject: Re: State-of-the-Art in Physics by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBPN3J502855; >> > THE STATE-OF-THE-ART IN PHYSICS > > There is similarity and distinction between mathematics and physics. > They are similar in the sense that they both study the structure, > properties and behavior of their respective subject matter. The > difference lies in their subject matter: that of mathematics is the > representation of thought, making it a language, and that of physics > is nature, making it a science. Both suffer from similar defects: > mathematical spaces and their concepts are ill-defined and nature and > physical concepts are also ill-defined. >> > > That's one of the reasons The Smart Model Theory, was developed. >>Physics >is full of ill-defined things like, electron orbitals, and electron >>change >>of >orbital to show various lines on the line spectra, and uncertainty >>etc... >>. > > The Smart Model has accurately predicted the structures now observed >>from >real atomic images, like for example oxygen. The Smart Model predicted >>oxygen >was a ring. QM said it was a sphere. Now they observe oxygen rings on, >>PdO. >>It >looks like this from real atomic images showing oxygen attached to Pd >>like >>this >on the outer layers of Pd, > > ooooooooooooooooooooo > oooooo oooooooooooooo > oooooooooooo > ooooooo ooooooooo > oooooooooooooo > ooooooooooooooooo >oooooooooooooooooo > > >Smart's Alt. Physics News Group >ht tp://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >S. Enterprize (Science Journal) >http://smart1234.s-enterprize.com / >> >>basic constituent of matter? >> >>E. E. Escultura > >>The >>Spiral >Fields, in an intelligent logic way to keep the proton perpetually moving >>for >an upper mean life of about 10^30 years. > >with Helix Spiral Spinning Fields, > > > CW spin > ( ) sub-proton > ( ) > ((((( ))))) > (((((((((( )))))))))) Neutral Zone > ((((( ))))) made of 3 quarks > ( ) > ( ) sub-anti-proton > CCW spin > > This is the internal view. The external view is another Helix Spiral >Spinning field spinning in the direction of the matter field. The >>resonate >frequency. When additional energy is absorbed, a photon is released within >>the >Neutral zone. The Neutral Zone prevents the matter and anti-matter from >colliding. The quarks oscillate producing a constant line spectra. This >constant resonance also keeps the mass constant, which is just a high >sub-atomic pressure zone in the Neutral Zone. > > You may ask what keeps the proton spinning. The EM fields produced >>within >>the >high pressure neutral zone sets up a sub-atomic resistance. The quarks >>sets >>up >a sub-atomic capacitance, and the main internal Helix Spiral Field sets up >sub-atomic inductance. So what you have is basically a RCL sub-atomic >>electric >oscillator circuit. The basic sub-atomic voltage is the potential >>difference >between the matter and anti-matter side which is for a proton at rest >>about >>938 >MeV. > > I made calculations comparing a mitochondria proto-motive potential >>with >this proton set up and I end up with the same basic current found in a >mitochondria, which is the power source for a cell and the RNA and DNA. > > The oscillator field produces the same line spectra for hydrogen. The >>line >spectra is really the convergence of three oscillator interactions at the >Neutral Zone core. They produce certain lines when a cfft ( complex fast >fourier tranform) is taken for these oscillators. Using these oscillators >>fft, >the total line spectra can be produced for hydrogen. > And the same goes for helium and all the other elements. Except there >>is >>a >Periodic Table of Elements. > The Smart Model is really more accurate than the QM Model or the >>Standard >Model and is in agreement at all levels of analysis, including chemistry, >>math, >physics, classicle physics, stellar, galactic, and universal levels. > The Smart Model also has a unified universal field theory that unifies >>all >fields in the universe, not just the atomic level that Einstein was >>working >>on. > > >Smart's Alt. Physics News Group >ht tp://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >S. Enterprize (Science Journal) >http://smart1234.s-enterprize.com / > >>Please give us the central ideas of your theory. For example, (1) What is >>the >>basic constituent of matter and (2) prove that it is indestructibel . (3) >>Well-define the electron, proton and neutron. >>(4) What are the fundamental physical principles of your theory? >> >>E. E. Escultura > Just go to my Website and click, Home of The Smart Model. Then go to >pages 2 and 3. >Smart's Alt. Physics News Group >ht tp://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >S. Enterprize (Science Journal) >http://smart1234.s-enterprize.com / >>can see that your theory is probably the most advanced conventional model of >>nature, that is, it DESCRIBES nature geometrically and in terms of >>mathematical equations, functions, etc. >>However, it cannot explain natural phenomena. Moreover, predictions are > Check this out. It does. Look at things in nature. >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rab bits >based >>on analogy between structures or properties of distinct and, therefore, >>independent spaces, one a mathematical space which is man-made and the other, >>physical space. >>Just as I did in mathematics where I required every mathematical space and >>its concepts to be well-defined by a set of axioms, I also require nature to >>be well-defined by its laws. Then a > It is. The Smart Model CAN go into these levels of details. >physical concept is well-defined if its >>existence, constituent, behavior and interactions are specified by the laws >>of nature. As in mathematics where a proof or explanation is justified by the >>axioms, proof of physical principle or explanation of natural phenomena must >>follow from the laws of nature. This > Just as the LINK shown above shows. >requires a new methodology that I call >>dynamic modeling, it EXPLAINS nature in terms of its laws. Then the task of >>the scientist is no longer that of finding accurate mathematical model of >>natural phenomena but one of finding the laws of nature that explain natural >>phenomena. Then, the accuracy of > Look at this. >http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html#300 > This Smart Model uses basically the same type spirals and Golden numbers >etc. found in math, including prime numbers, and numbers generated from an >atomic level, Fibonacci Spiral, which is part of the Helix Spiral Spinning >Interacting Field, The Smart Model uses. >predictions will ultimately rest on the laws >>of nature. This new methodology made the difference in my solution of the >>gravitational n-body problem in 1997 (Nonlinear Analysis, Vol. 30, No. 8). >>By the way, does your theory accommodate the existence of dark matter? This > The Smart Model doesn't really use dark matter unless you might mean >excessive left over matter from dead stars etc, which make additional >gravitational forces. >>is assured by the first law of thermodynamics, which is a special case of my >>Analysis in Engineering Systems, Vol. 7, No. 1, 2001)), in tandem with the >>observation by the Hubble that matter forms steadily in the supposedly empty >>space that congeals into stars at the rate of one star/minute. If this is the >>case, then the theory must have appropriate natural laws governing conversion >>from dark to ordinary or visible matter and conversely. > Why of course. When new stars form from surrounding cosmic dust, some of this >dark matter is included. There are even old meteors that are about 1 billion >years old. This is included with asteriods and other large sized matter left >over from dead stars and exploding stars with old solar systems in the >galaxies. > The Smart Model has even discovered what it thinks is stars that never burn >out. These are very large massive stars that use lithium to deuterium fusion >and vise versa, in it's atomic fusion reactions while the inner core of the sun >remains the same. >>E. E. Escultura >>University of the Philippines >Smart's Alt. Physics News Group >ht tp://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 >S. Enterprize (Science Journal) >http://smart1234.s-enterprize.com / Actually, dynamic modeling that explains or models nature in terms of is laws and conventional modeling that describes nature in terms of mathematical equations, functions, etc. are complementary. The two together provides a powerful tool for the pursuit of physics. Let me offer some examples: 1) Through observation, measurement and computation, conventional modeling has been able to establish that our universe is expanding radially at the rate of 10^20 km/sec and that expansion is accelerated at the rate of 1/10^10 km/sec/sec implying that our universe is still evolving towards its peak of power as a superásuper galaxy. Even its present size is known: 10^10 light years across. Its core, the collected mass around its vortex eye discovered by French astronomers in 1994 is a tightly packed cocoon-shaped galaxy cluster 650 light years across. However, the determination that our universe is a huge galaxy and why it is expanding are provided by the laws of nature that I have discovered through dynamic modeling the laws of nature that well-define our universe, what it consists of and its behavior. Moreover, dynamic modeling explains what every cosmological body except debris like asteroid spins. (Details in the paper, Dynamic modeling of chaos and turbulence, Proc. 4th ! World Congress of Nonlinear Analysts, July, Orlando, to be published as special issue of Nonlinear Analysis by Elsevier Science, Ltd., in February) 2) Another physical concept or phenomenon that mathematical physics cannot well-define through conventional modeling alone is a black hole. It is a massive cluster of non-agitated superstrings that accumulate in the eye of some cosmological vortex like a star or galaxy. Since it is dark matter, it does not suck matter around it contrary to popular belief. It is the eye of the vortex that nurtures, collects and builds that does. >on analogy between structures or properties of distinct and, therefore, >independent spaces, one a mathematical space which is man-made and the other, >physical space. >Just as I did in mathematics where I required every mathematical space and >its concepts to be well-defined by a set of axioms, I also require nature to >be well-defined by its laws. Then a It is. The Smart Model CAN go into these levels of details. physical concept is well-defined if its >existence, constituent, behavior and interactions are specified by the laws >of nature. As in mathematics where a proof or explanation is justified by the >axioms, proof of physical principle or explanation of natural phenomena must >follow from the laws of nature. This Just as the LINK shown above shows. requires a new methodology that I call >dynamic modeling, it EXPLAINS nature in terms of its laws. Then the task of >the scientist is no longer that of finding accurate mathematical model of >natural phenomena but one of finding the laws of nature that explain natural >phenomena. Then, the accuracy of Look at this. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html#300 This Smart Model uses basically the same type spirals and Golden numbers etc. found in math, including prime numbers, and numbers generated from an atomic level, Fibonacci Spiral, which is part of the Helix Spiral Spinning Interacting Field, The Smart Model uses. predictions will ultimately rest on the laws >of nature. This new methodology made the difference in my solution of the >gravitational n-body problem in 1997 (Nonlinear Analysis, Vol. 30, No. 8). >By the way, does your theory accommodate the existence of dark matter? This The Smart Model doesn't really use dark matter unless you might mean excessive left over matter from dead stars etc, which make additional gravitational forces. >is assured by the first law of thermodynamics, which is a special case of my >Analysis in Engineering Systems, Vol. 7, No. 1, 2001)), in tandem with the >observation by the Hubble that matter forms steadily in the supposedly empty >space that congeals into stars at the rate of one star/minute. If this is the >case, then the theory must have appropriate natural laws governing conversion >from dark to ordinary or visible matter and conversely. >Why of course. When new stars form from surrounding cosmic dust, some of this >dark matter is included. There are even old meteors that are about 1 billion >years old. This is included with asteriods and other large sized matter left over from dead stars and exploding stars with old solar systems in the galaxies. > The Smart Model has even discovered what it thinks is stars that never burn out. These are very large massive stars that use lithium to deuterium fusion and vise versa, in it's atomic fusion reactions while the inner core of the sun remains the same. http://home.iprimus.com.au/pidro/ === Subject: brainteaser an ant, traveling at uniform speed, takes one minute to crawl from one end of a ruler to the other and fall off. when two ants run into each other, the rule is that each turns around and goes the other way. if we throw 5 ants at random onto the ruler (they all hit the ruler at the same time, and then choose a direction to crawl at random, every one of them always traveling at the same uniform speed -- 1 ruler length per minute), what is the least amount of time needed to guarantee that all 5 ants have fallen off the ruler? I believe the answer is 1 min ... but can someone show me how this can be proven? === Subject: Re: brainteaser !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(5eZ41to5f%E@'ELIi $t^ VcLWP@J5p^rst0+('>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw > an ant, traveling at uniform speed, takes one minute to crawl from > one end of a ruler to the other and fall off. when two ants run into > each other, the rule is that each turns around and goes the other > way. if we throw 5 ants at random onto the ruler (they all hit the > ruler at the same time, and then choose a direction to crawl at > random, every one of them always traveling at the same uniform speed > -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? Your use of the word random is absurd. No randomness is involved here at all. You are asking for the configuration with the longest duration, period. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from > one end of a ruler to the other and fall off. when two ants run into > each other, the rule is that each turns around and goes the other > way. if we throw 5 ants at random onto the ruler (they all hit the > ruler at the same time, and then choose a direction to crawl at > random, every one of them always traveling at the same uniform speed > -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > Your use of the word random is absurd. No randomness is involved > here at all. You are asking for the configuration with the longest > duration, period. He's asking for *a* configuration with the longest duration, only because the problem is solvable. If a random walk through a network of 100 intersections goes from A to B, what is the least amount of time guaranteed to be at B? is not asking for the longest duration because generally it's not possible to calculate it. There are other techniques to find solutions than calculating a witness. If I toss a coin what's the result? There's nothing random about it. Herc === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from one end of a > ruler to the other and fall off. when two ants run into each other, the rule is > that each turns around and goes the other way. if we throw 5 ants at random > onto the ruler (they all hit the ruler at the same time, and then choose a > direction to crawl at random, every one of them always traveling at the same > uniform speed -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > I believe the answer is 1 min ... but can someone show me how this can be > proven? I have read this somewhere but I can't recall where it was. I found it rather brilliant :-) It can be proven that after at most one minute the rule is cleared of all its ants, by simply restating the problem by having the ants *pass* each other when they meet. After all, looking from a great enough distance, you cannot see any difference between bouncing and passing. Likewise! Dirk Vdm === Subject: Re: brainteaser Dirk Van de moortel > an ant, traveling at uniform speed, takes one minute to crawl from one end of a > ruler to the other and fall off. when two ants run into each other, the rule is > that each turns around and goes the other way. if we throw 5 ants at random > onto the ruler (they all hit the ruler at the same time, and then choose a > direction to crawl at random, every one of them always traveling at the same > uniform speed -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > I believe the answer is 1 min ... but can someone show me how this can be > proven? > I have read this somewhere but I can't recall where it > was. I found it rather brilliant :-) > It can be proven that after at most one minute the rule is > cleared of all its ants, by simply restating the problem by > having the ants *pass* each other when they meet. After > all, looking from a great enough distance, you cannot see > any difference between bouncing and passing. And why shouldn't they pass each other--nothing was said about the width of the ruler being restricted. If they always bounce when they meet, I can only deduce they are speaking to each other and one takes an _order_ to reverse from the other--very intelligent. Or maybe 'tis just due to pheromones. ...tonyC > Likewise! > Dirk Vdm === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from one > end of a ruler to the other and fall off. when two ants run into each > other, the rule is that each turns around and goes the other way. if we > throw 5 ants at random onto the ruler (they all hit the ruler at the > same time, and then choose a direction to crawl at random, every one of > them always traveling at the same uniform speed -- 1 ruler length per > minute), what is the least amount of time needed to guarantee that all 5 > ants have fallen off the ruler? Have you any sense the intelligence of ants? They ain't going to fall off, they's gonna look around. They might even walk along the vertical edge of the ruler. When ants do march in a line, those meeting have brief antenna to antenna talk subsequently proceeding in their original directions. Those ant brains are too smart to play your stupid game. I suggest you use some obediant dolts, like suicide bombers, frothing at the mouth fundamentalists, or faithful Republicans. They're much more willing to fall off the edge of the world. > I believe the answer is 1 min ... but can someone show me how this can be > proven? Bible says 2000 years everybody falls off. Bah Humbug! Ho! Ho! Ho! === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from one end of > ruler to the other and fall off. when two ants run into each other, the rule > is > that each turns around and goes the other way. if we throw 5 ants at random > onto the ruler (they all hit the ruler at the same time, and then choose a > direction to crawl at random, every one of them always traveling at the same > uniform speed -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > I believe the answer is 1 min ... but can someone show me how this can be > proven? Proving it only requires that some combination of positions and directions be found which takes one minute to clear all the ants, and such an arrangement is trivially simple to construct. === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from one end of > a > ruler to the other and fall off. when two ants run into each other, the rule > is > that each turns around and goes the other way. if we throw 5 ants at random > onto the ruler (they all hit the ruler at the same time, and then choose a > direction to crawl at random, every one of them always traveling at the same > uniform speed -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > I believe the answer is 1 min ... but can someone show me how this can be > proven? > Proving it only requires that some combination of positions and > directions be found which takes one minute to clear all the ants, and > such an arrangement is trivially simple to construct. I can make an arrangement where they all fall off in one second. The least amount of time you can state that the ruler will always be empty afterwards. i.e. the MAXIMUM time the ants stay on. Typical random arrangement, 20 . = 60 seconds, 1 . = 3 seconds. a> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VALE! . . . . . . a> . . . . . . . . . .a> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VALE! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VALE! VALE! 20 steps = 60 seconds! Herc === Subject: Re: brainteaser > an ant, traveling at uniform speed, takes one minute to crawl from one end of a > ruler to the other and fall off. when two ants run into each other, the rule is > that each turns around and goes the other way. if we throw 5 ants at random > onto the ruler (they all hit the ruler at the same time, and then choose a > direction to crawl at random, every one of them always traveling at the same > uniform speed -- 1 ruler length per minute), what is the least amount of time > needed to guarantee that all 5 ants have fallen off the ruler? > I believe the answer is 1 min ... but can someone show me how this can be > proven? obviously, zero. Unless your ants have physical size. === Subject: Re: brainteaser <336qleF3sjr5rU1@individual.net> Of course the ants have sizes. So depending on the length of the each of the 5 ants, the least time should be: (the total length of the 5 ants plus 4 minimum spaces between them so that no ant would bump into another) divided by (the uniform speed). Here, the 1st ant landed at the edge of one end of the ruler. Simultaneous to that, the 2nd, 3rd, 4th, and 5th ants landed closely by, in one line, separated only by the minimum space to avoid any bumping while crawling. And they all crawl in the same direction toward the near end of the ruler. === Subject: Re: brainteaser > Of course the ants have sizes. > So depending on the length of the each of the 5 ants, the least time > should be: (the total length of the 5 ants plus 4 minimum spaces > between them so that no ant would bump into another) divided by (the > uniform speed). > Here, the 1st ant landed at the edge of one end of the ruler. > Simultaneous to that, the 2nd, 3rd, 4th, and 5th ants landed closely > by, in one line, separated only by the minimum space to avoid any > bumping while crawling. And they all crawl in the same direction toward > the near end of the ruler. agreed, however he said, least time to guarantee all have fallen off. Guarantee implies any initial conditions of the ants. This implies the Max time. Which would be about 2 min. Does he mean Max where he says least? === Subject: does WGN(white Gaussian noise) imple zero mean? Hi all, I read through several books but did not get clarification on whether WGN(white Gaussian noise process) imply zero mean or not... Another confusion I have is that the definition of WGN is it has flat power spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its autocorrelation function, I don't see how people say the power of this noise process is E((x(t))^2)=sigma_x, something like that... the power should be infinite, right? === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > Hi all, > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, something like that... the power should be > infinite, right? That's because I believe most of the time the PSD for white noise is quoted incorrectly. It should be sigma squared/(fs) and it is flat from fs/2 to -fs/2 where fs is the sampling freq.The area under the PSD is the total average power or sigma squared. (including negative frequencies). If you time-average the data (noise) you should get a variance of sigma squared (assuming the mean to be zero).Hence the time average (sum of squares/N) is the same as the statistical average E[x^2]. As for autocorrelation, the impulse is there to denote that it is just a spike.If you take the Fourier Transform of the autocorrleation function you should get PSD (Wiener-Kinchen Theorem). So you can work it out for yourself - however - please note the difference between PSD and the AREA UNDER IT which is the total average power. Country Chiel === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > Hi all, > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... OK. Think. Hmm. The definition of a white noise process is that the PSD is 1 everywhere. OK, I understand that. If I know the PSD of a function I can find the expected power between any two frequencies by just integrating the PSD over that interval. OK, I've read my books, I understand that. Now, DC means the frequency interval between 0 and 0 (technically between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, something like that... the power should be > infinite, right? For a truly white PSD the power is infinite (see, I'm not raking you over the coals for this -- this is actually a bit of a brain twister and therefore not a blindingly obvious question). This is actually the mathematical difficulty that led Plank to his discovery of black-body radiation -- before Plank you had to just describe thermal noise in a resistor or whatnot as white noise, and shrug your shoulders when the question of infinite power came up. So for all practical purposes you should remember that white noise of any sort is a mathematical fiction, and only it to predict the responses of physical systems who's bandwidths are much lower than the bandwidth limitation of the noise you have at hand. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: does WGN(white Gaussian noise) imple zero mean? windows-nt) >> Hi all, >> I read through several books but did not get clarification on >> whether WGN(white Gaussian noise process) imply zero mean or not... > OK. Think. > Hmm. The definition of a white noise process is that the PSD is 1 > everywhere. OK, I understand that. > If I know the PSD of a function I can find the expected power between > any two frequencies by just integrating the PSD over that interval. > OK, I've read my books, I understand that. > Now, DC means the frequency interval between 0 and 0 (technically > between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! Hey Tim, You get the same result when integrating between 1- and 1+, or 253,392- and 253,392+, etc., and we know have power at there. What have you answered, then? -- % Randy Yates % With time with what you've learned, %% Fuquay-Varina, NC % they'll kiss the ground you walk %%% 919-577-9882 % upon. %%%% % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr === Subject: Re: does WGN(white Gaussian noise) imple zero mean? >Hi all, >I read through several books but did not get clarification on >whether WGN(white Gaussian noise process) imply zero mean or not... >>OK. Think. >>Hmm. The definition of a white noise process is that the PSD is 1 >>everywhere. OK, I understand that. >>If I know the PSD of a function I can find the expected power between >>any two frequencies by just integrating the PSD over that interval. >>OK, I've read my books, I understand that. >>Now, DC means the frequency interval between 0 and 0 (technically >>between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! > Hey Tim, > You get the same result when integrating between 1- and 1+, or > 253,392- and 253,392+, etc., and we know have power at there. > What have you answered, then? Well, _I've_ answered that there's no DC content (which is another way of saying zero mean), when you take DC to it's mathematical limit (note that white noise will appear to have DC content if you only observe it for a finite amount of time, such as the time from the big bang to right now). _You've_ extended this to show that you can pick any one, zero-bandwidth, filter and find no energy there. Hopefully I've also pointed out to Kiki that he has all this information at his fingertips if he'd just collate, think, and use a pencil and paper every once in a while. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: does WGN(white Gaussian noise) imple zero mean? <10su3ofarheof22@corp.supernews.com> windows-nt) >>Hi all, >>I read through several books but did not get clarification on >>whether WGN(white Gaussian noise process) imply zero mean or not... >OK. Think. >Hmm. The definition of a white noise process is that the PSD is 1 >everywhere. OK, I understand that. >If I know the PSD of a function I can find the expected power between >any two frequencies by just integrating the PSD over that interval. >OK, I've read my books, I understand that. >Now, DC means the frequency interval between 0 and 0 (technically >between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! >> Hey Tim, >> You get the same result when integrating between 1- and 1+, or >> 253,392- and 253,392+, etc., and we know have power at there. What >> have you answered, then? > Well, _I've_ answered that there's no DC content (which is another way > of saying zero mean), when you take DC to it's mathematical limit > (note that white noise will appear to have DC content if you only > observe it for a finite amount of time, such as the time from the big > bang to right now). _You've_ extended this to show that you can pick > any one, zero-bandwidth, filter and find no energy there. No, you've shown that there is no power there. There is indeed energy there since, for white noise, Sxx(w) at w = w0 is strictly greater than zero for any value of w0 (including 0), and the units of power spectral density are [joules] ([watts/Hz] == [joules]). One obtains power upon integration of the Sxx(w) (no matter how small of an integration interval is chosen) since int_{w_0-}^{w_0+} Sxx(w) dw has units of [joules] * [1/seconds], i.e., power. > Hopefully I've also pointed out to Kiki that he has all this > information at his fingertips if he'd just collate, think, and use a > pencil and paper every once in a while. If you confuse me and I've had two classes in it, I can't imagine what's going on in kiki's mind. It is very possible that my mind is screwed on wrong - if you think so, show me where my thinking has gone astray. -- % Randy Yates % With time with what you've learned, %% Fuquay-Varina, NC % they'll kiss the ground you walk %%% 919-577-9882 % upon. %%%% % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr === Subject: Re: does WGN(white Gaussian noise) imple zero mean? >> >> >> >Hi all, >I read through several books but did not get clarification on >whether WGN(white Gaussian noise process) imply zero mean or not... >> >>OK. Think. >> >>Hmm. The definition of a white noise process is that the PSD is 1 >>everywhere. OK, I understand that. >> >>If I know the PSD of a function I can find the expected power between >>any two frequencies by just integrating the PSD over that interval. >>OK, I've read my books, I understand that. >> >>Now, DC means the frequency interval between 0 and 0 (technically >>between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! >Hey Tim, >You get the same result when integrating between 1- and 1+, or >253,392- and 253,392+, etc., and we know have power at there. What >have you answered, then? >>Well, _I've_ answered that there's no DC content (which is another way >>of saying zero mean), when you take DC to it's mathematical limit >>(note that white noise will appear to have DC content if you only >>observe it for a finite amount of time, such as the time from the big >>bang to right now). _You've_ extended this to show that you can pick >>any one, zero-bandwidth, filter and find no energy there. > No, you've shown that there is no power there. There is indeed energy > there since, for white noise, Sxx(w) at w = w0 is strictly greater > than zero for any value of w0 (including 0), and the units of power > spectral density are [joules] ([watts/Hz] == [joules]). One obtains > power upon integration of the Sxx(w) (no matter how small of an > integration interval is chosen) since int_{w_0-}^{w_0+} Sxx(w) dw has > units of [joules] * [1/seconds], i.e., power. Oy -- good point. Geeze these limits-to-infinity things get tricky. There must be energy there because if you integrate a white noise process the variance of the result goes up with the integration time. But if you take the average of the white noise process (average = integral / integration time) then the variance goes _down_ with the integration time, eventually going to zero as the integration time goes to infinity. So; zero mean, infinite energy. >>Hopefully I've also pointed out to Kiki that he has all this >>information at his fingertips if he'd just collate, think, and use a >>pencil and paper every once in a while. > If you confuse me and I've had two classes in it, I can't imagine > what's going on in kiki's mind. It is very possible that my mind > is screwed on wrong - if you think so, show me where my thinking > has gone astray. I was confused about this stuff, too, and asking questions didn't clear it up. What _did_ clear it up (for the most part; see your comment above) was thinking about it. I had the advantage that I take long bike rides, and for some reason it really worked for me to ponder these questions while riding. This is why I'm trying to get the guy pulled away from Matlab simulations. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: does WGN(white Gaussian noise) imple zero mean? >> >> > > >> >> >> >Hi all, >I read through several books but did not get clarification on >whether WGN(white Gaussian noise process) imply zero mean or not... >> >>OK. Think. >> >>Hmm. The definition of a white noise process is that the PSD is 1 >>everywhere. OK, I understand that. >> >>If I know the PSD of a function I can find the expected power between >>any two frequencies by just integrating the PSD over that interval. >>OK, I've read my books, I understand that. >> >>Now, DC means the frequency interval between 0 and 0 (technically >>between 0- and 0+). Integrating 1 between 0 and 0 I get -- ZERO! WOW! > >Hey Tim, >You get the same result when integrating between 1- and 1+, or >253,392- and 253,392+, etc., and we know have power at there. What >have you answered, then? >> >>Well, _I've_ answered that there's no DC content (which is another way >>of saying zero mean), when you take DC to it's mathematical limit >>(note that white noise will appear to have DC content if you only >>observe it for a finite amount of time, such as the time from the big >>bang to right now). _You've_ extended this to show that you can pick >>any one, zero-bandwidth, filter and find no energy there. > No, you've shown that there is no power there. There is indeed energy > there since, for white noise, Sxx(w) at w = w0 is strictly greater > than zero for any value of w0 (including 0), and the units of power > spectral density are [joules] ([watts/Hz] == [joules]). One obtains > power upon integration of the Sxx(w) (no matter how small of an > integration interval is chosen) since int_{w_0-}^{w_0+} Sxx(w) dw has > units of [joules] * [1/seconds], i.e., power. > Oy -- good point. Geeze these limits-to-infinity things get tricky. If I had a dime for every time I posted an erroroneous statement in this newsgroup... > There must be energy there because if you integrate a white noise > process the variance of the result goes up with the integration > time. But if you take the average of the white noise process (average > = integral / integration time) then the variance goes _down_ with the > integration time, eventually going to zero as the integration time > goes to infinity. Yes, agreed. > So; zero mean, infinite energy. No, I don't agree! See the post I'm about to make in response to my first response to kiki. > I was confused about this stuff, too, and asking questions didn't > clear it up. What _did_ clear it up (for the most part; see your > comment above) was thinking about it. I had the advantage that I take > long bike rides, and for some reason it really worked for me to ponder > these questions while riding. Yup, I'm a fello ponderer too. So much so that many people think I'm an idiot (what difference does the wherefore and the why make? just DO IT!). > This is why I'm trying to get the guy pulled away from Matlab > simulations. YES! An excellent goal. Personally I have found Matlab to be useful in learning only after considerable effort has already been spent with pencil and paper (and bicycle, if that's your thing), and then only sometimes. It's off-topic, but it is this exact sort of thing, this sort of the deeper brain cells aren't exercised with a computer thing, that makes me boil every time I hear about what a good thing computers are in school and how smart kids are these days because they know how to use a computer. Bah! -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124 === Subject: Re: does WGN(white Gaussian noise) imple zero mean? ... > So for all practical purposes you should remember that white noise of > any sort is a mathematical fiction, and only it to predict the responses > of physical systems who's bandwidths are much lower than the bandwidth > limitation of the noise you have at hand. Man, I wish I had had you for a teacher, back when it mattered! Jerry -- Engineering is the art of making what you want from things you can get. .88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N 210N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N21 0N.88N.88N.88N.88N === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... WGN does not imply zero mean. It only says that the noise is gaussian distributed and the rv from any two different time instances of the process are always uncorrelated. But noise is always assumed to be zero mean because it is usually additive and hence you can subtract the mean to make it zero mean. > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, something like that... the power should be > infinite, right? Talking about the power of a random process is not precise at all. sigma^2 is the variance of the gaussian pdf, and the power spectral density has an amplitude that is sigma^2/2 flat. The power is actually the area under power spectral density and is infinite, literally. Hope it helps. Prasanna. === Subject: Re: does WGN(white Gaussian noise) imple zero mean? windows-nt) > Hi all, > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... Hi Kiki, Now you've got me wondering. On one hand, I've heard the term zero-mean additive white Gaussian noise many times, but on the other hand, white implies a flat PSD, which in term implies that there is some power at DC. So I can't answer your question. > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, Rxx(t) is defined to be Rxx(tau)= E[x(t)*x(t-tau)] for a real random process x(t). Then, by definition, E[x^2(t)] = E[x(t) * x(t-0)] = Rxx(0) = undefined (infinity) when Rxx(t) = delta(t). Thus you're contradicting yourself somewhat. A truly white-noise process does have infinite power (hence the Dirac delta function in the autocorrelation), but most transistors I know of burn out after a few gigawatts, so we usually speak of a band-limited white noise process, i.e., a process which has a PSD Sxx(w) = c, |w| < a, and in which case the power is finite and Rxx(0) = a*c/pi. -- % Randy Yates % She's sweet on Wagner-I think she'd die for Beethoven. %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and %%% 919-577-9882 % Verdi's always creepin' from her room. %%%% % Rockaria, *A New World Record*, ELO http://home.earthlink.net/~yatescr === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > Hi all, > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... > Hi Kiki, > Now you've got me wondering. On one hand, I've heard the term zero-mean > additive white Gaussian noise many times, but on the other hand, white > implies a flat PSD, which in term implies that there is some power at DC. > So I can't answer your question. Kiki I hope you're reading this new post, I can now partially answer your question. In order to do this, first realize that when someone speaks of a zero-mean, white Gaussian noise process, they're talking about a random process with an underlying distribution, i.e., for each point in time t, the random process x(t) has a specific probability density function f(t, s). IT IS THIS UNDERLYING PDF THAT IS ZERO-MEAN. However, that still doesn't completely resolve the issue (at least in my mind it doesn't). A random process is ergodic if its time-wise statistics are the same as its ensemble-wise statistics. So we have a dilemma when postulating a zero-mean, white, ergodic random noise process because ensemble-wise the mean is zero while time-wise the mean is non-zero (since there's non-zero energy at DC). I still don't know how to resolve THIS problem! --Randy > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, > Rxx(t) is defined to be > Rxx(tau)= E[x(t)*x(t-tau)] > for a real random process x(t). Then, by definition, > E[x^2(t)] = E[x(t) * x(t-0)] > = Rxx(0) > = undefined (infinity) > when Rxx(t) = delta(t). Thus you're contradicting yourself somewhat. > A truly white-noise process does have infinite power (hence the Dirac > delta function in the autocorrelation), but most transistors I know > of burn out after a few gigawatts, so we usually speak of a band-limited > white noise process, i.e., a process which has a PSD Sxx(w) = c, |w| < a, > and in which case the power is finite and Rxx(0) = a*c/pi. > -- > % Randy Yates % She's sweet on Wagner-I think she'd die for Beethoven. > %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and > %%% 919-577-9882 % Verdi's always creepin' from her room. > %%%% % Rockaria, *A New World Record*, ELO > http://home.earthlink.net/~yatescr -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124 === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > Hi all, > > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... > Hi Kiki, > Now you've got me wondering. On one hand, I've heard the term zero-mean > additive white Gaussian noise many times, but on the other hand, white > implies a flat PSD, which in term implies that there is some power at DC. > So I can't answer your question. > Kiki I hope you're reading this new post, > I can now partially answer your question. In order to do this, first > realize that when someone speaks of a zero-mean, white Gaussian noise > process, they're talking about a random process with an underlying > distribution, i.e., for each point in time t, the random process x(t) > has a specific probability density function f(t, s). IT IS THIS > UNDERLYING PDF THAT IS ZERO-MEAN. Yup. Note that Gaussian white noise doesn't exist, since its variance would be infinite. But if you allow distrubutions with infinite variance (thus allowing delta functions), then ok ... > However, that still doesn't completely resolve the issue (at least in > my mind it doesn't). A random process is ergodic if its time-wise > statistics are the same as its ensemble-wise statistics. So we have a First note that white noise is ergodic since it's stationary and the covariance vanishes at infinity. > dilemma when postulating a zero-mean, white, ergodic random noise > process because ensemble-wise the mean is zero while time-wise the > mean is non-zero (since there's non-zero energy at DC). I still don't > know how to resolve THIS problem! I don't get how it follows that the time-average (mean) would be infinite? R(0) being infinite doesn't imply that the mean should be infinite. Wilbert === Subject: Re: does WGN(white Gaussian noise) imple zero mean? when T->inf, we got a finite ENERGY, but it doesn't mean the average Power isn't zero. E=Lim P*T, it is undetermined by 0*inf in mathematics. T->inf actually the power density at DC (or other single frequency point) which you had noticed it has energy unit is the engergy of the ensemble average of the time average signal. apply FT to autocorrelation , and let f =0, we get PSD(0) = lim T* (1/T * E(int(x(t)))^2, T->inf. > Hi all, > > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... > Hi Kiki, > Now you've got me wondering. On one hand, I've heard the term zero-mean > additive white Gaussian noise many times, but on the other hand, white > implies a flat PSD, which in term implies that there is some power at DC. > So I can't answer your question. > Kiki I hope you're reading this new post, > I can now partially answer your question. In order to do this, first > realize that when someone speaks of a zero-mean, white Gaussian noise > process, they're talking about a random process with an underlying > distribution, i.e., for each point in time t, the random process x(t) > has a specific probability density function f(t, s). IT IS THIS > UNDERLYING PDF THAT IS ZERO-MEAN. > However, that still doesn't completely resolve the issue (at least in > my mind it doesn't). A random process is ergodic if its time-wise > statistics are the same as its ensemble-wise statistics. So we have a > dilemma when postulating a zero-mean, white, ergodic random noise > process because ensemble-wise the mean is zero while time-wise the > mean is non-zero (since there's non-zero energy at DC). I still don't > know how to resolve THIS problem! > --Randy > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, > Rxx(t) is defined to be > Rxx(tau)= E[x(t)*x(t-tau)] > for a real random process x(t). Then, by definition, > E[x^2(t)] = E[x(t) * x(t-0)] > = Rxx(0) > = undefined (infinity) > when Rxx(t) = delta(t). Thus you're contradicting yourself somewhat. > A truly white-noise process does have infinite power (hence the Dirac > delta function in the autocorrelation), but most transistors I know > of burn out after a few gigawatts, so we usually speak of a band-limited > white noise process, i.e., a process which has a PSD Sxx(w) = c, |w| < a, > and in which case the power is finite and Rxx(0) = a*c/pi. > -- > % Randy Yates % She's sweet on Wagner-I think she'd die for Beethoven. > %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and > %%% 919-577-9882 % Verdi's always creepin' from her room. > %%%% % Rockaria, *A New World Record*, ELO > http://home.earthlink.net/~yatescr > -- > Randy Yates > Sony Ericsson Mobile Communications > Research Triangle Park, NC, USA > randy.yates@sonyericsson.com, 919-472-1124 === Subject: Re: does WGN(white Gaussian noise) imple zero mean? > Hi all, > I read through several books but did not get clarification on whether > WGN(white Gaussian noise process) imply zero mean or not... Zero mean. > Another confusion I have is that the definition of WGN is it has flat power > spectrum density, let's say S(f)=1, then Rx(t)=delta(t) is its > autocorrelation function, I don't see how people say the power of this noise > process is E((x(t))^2)=sigma_x, something like that... the power should be > infinite, right? Power cannot be infinite, unless you have identical waveforms for autocorrelation peak. === Subject: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? Hi all, Do you have a simple way of roughly estimate the max freuqency in a plot of data? For example, suppse I have collect a trace of data about one week's raining amount... I have to decide how much is the Nyquist sampling rate and how many samples do I need... how do I estimate the max frequency in the rainning data roughly? If I used Matlab to do data spectrum plot of the past a few years and find the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist rate to be 2 cycle per day, i.e. I measure twice data a day... of the function x(t)... But now I want to measure once a day, but sampling both x(t) and x'(t) (derivitative) once per day... for what kind of x(t) can I do this kind of lazy measurement sampling? How do I reconstruct the original function x(t) by having the x(t) and x'(t) samples for one measurement per day? Can I reduce the measurements to once per week, by sampling x(t), x'(t) , x''(t), ... till the 14th derivative? What are the reasons why this sampling/interpolation scheme has not been used in practice? Any ideas? === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? Some suggestions below: Fred > Hi all, > Do you have a simple way of roughly estimate the max freuqency in a plot > of data? > For example, suppse I have collect a trace of data about one week's > raining amount... I have to decide how much is the Nyquist sampling rate > and how many samples do I need... how do I estimate the max frequency in > the rainning data roughly? You could compute a Fourier Transform of the data. That would probably mean computing an FFT using a very high sample rate. Under the assumption that you're using a rainfall guage, it integrates the individual drops and even some of the small squalls. So, the individual raindrops are not the issue here. > If I used Matlab to do data spectrum plot of the past a few years and find > the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist > rate to be 2 cycle per day, i.e. I measure twice data a day... of the > function x(t)... How often was the data sampled in the first place? What is a cycle in this context? I don't know what -1 cycle means - that the rain was falling up? > But now I want to measure once a day, but sampling both x(t) and x'(t) > (derivitative) once per day... for what kind of x(t) can I do this kind of > lazy measurement sampling? What is x(t)? What was measured? Is it a rainfall guage? > How do I reconstruct the original function x(t) by having the x(t) and > x'(t) samples for one measurement per day? It probably isn't too much of a stretch to say: you can't > Can I reduce the measurements to once per week, by sampling x(t), x'(t) , > x''(t), ... till the 14th derivative? > What are the reasons why this sampling/interpolation scheme has not been > used in practice? If you have a function that is nicely defined mathematically, then in theory you might be able to do this. In that case you'd be using a mathematical manipulation to go from one set of numbers to another. Maybe that's properly called a mapping. However, in the real world you don't have such a nice math function and using the derivatives don't work for a number of reasons. One of those reasons is that the underlying data is from a random process. Another is that there is likely noise in real data - which adds more randomness. === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? ... > If you have a function that is nicely defined mathematically, then in theory > you might be able to do this. In that case you'd be using a mathematical > manipulation to go from one set of numbers to another. Maybe that's properly > called a mapping. > However, in the real world you don't have such a nice math function and > using the derivatives don't work for a number of reasons. One of those > reasons is that the underlying data is from a random process. Another is > that there is likely noise in real data - which adds more randomness. Aw, Fred! You let out the secret! Jerry -- Engineering is the art of making what you want from things you can get. .88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N 210N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N.88N21 0N.88N.88N.88N.88N === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? Have you a way to estimate the lowest em wave possible frequency -in general not just in a private case?? TIA Y.Porat ------------------------ === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > Hi all, > Do you have a simple way of roughly estimate the max freuqency in a plot > of data? > For example, suppse I have collect a trace of data about one week's raining > amount... I have to decide how much is the Nyquist sampling rate and how > many samples do I need... how do I estimate the max frequency in the > rainning data roughly? How did you collect the data in a way that you're sure you haven't already introduced sampling error? > If I used Matlab to do data spectrum plot of the past a few years and find > the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist > rate to be 2 cycle per day, i.e. I measure twice data a day... of the > function x(t)... You obviously aren't measuring rain in western Oregon. > But now I want to measure once a day, but sampling both x(t) and x'(t) > (derivitative) once per day... for what kind of x(t) can I do this kind of > lazy measurement sampling? In theory any x(t) for which two measurements per day would be adequate -- that means an x(t) which is _strictly_ bandlimited. > How do I reconstruct the original function x(t) by having the x(t) and x'(t) > samples for one measurement per day? I don't know offhand, so offhand I'd say you actually do some math before you ask the question. Then you'll not only know the answer, you'll also understand it. Start with the fact that x(t) is strictly bandlimited, and remember that the Taylor's series expansion figures in there somehow. > Can I reduce the measurements to once per week, by sampling x(t), x'(t) , > x''(t), ... till the 14th derivative? Sure -- if you are getting _really good_ derivatives, and if your x(t) is really truly bandlimited. Of course, if you want to get really good estimates of the derivatives from observation and you're not sure about the bandlimiting of x(t) then you need to sample it twice each day... > What are the reasons why this sampling/interpolation scheme has not been > used in practice? Think about it using _your own brain_ and you'll not only know the answer, but you'll also understand it. > Any ideas? Kiki, get out of Matlab, turn off your computer, get out of the lab, go outside, stare at the sky and THINK for a while, will you? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > Hi all, > Do you have a simple way of roughly estimate the max freuqency in a plot > of data? > For example, suppse I have collect a trace of data about one week's raining > amount... I have to decide how much is the Nyquist sampling rate and how > many samples do I need... how do I estimate the max frequency in the > rainning data roughly? > If I used Matlab to do data spectrum plot of the past a few years and find > the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist > rate to be 2 cycle per day, i.e. I measure twice data a day... of the > function x(t)... > But now I want to measure once a day, but sampling both x(t) and x'(t) > (derivitative) once per day... for what kind of x(t) can I do this kind of > lazy measurement sampling? > How do I reconstruct the original function x(t) by having the x(t) and x'(t) > samples for one measurement per day? > Can I reduce the measurements to once per week, by sampling x(t), x'(t) , > x''(t), ... till the 14th derivative? > What are the reasons why this sampling/interpolation scheme has not been > used in practice? > Any ideas? You can always find a way to push a system beyond it's applicable domain by ignoring the details needed to get it there. I'll go you one (or two) better. You can't sample rainfall at all because at any instant there's either a drop or there isn't, and sampling is about what happens at instants. When a drop hits, the derivative is, at the very least, very large, and between drops, it is zero. So sampling the derivative isn't much use. OK: lets get real. What we really do ... Wait: you tell me. How do you propose to collect your samples? What limitations do that sampling scheme impose? When you respect those limitations, is there still a dilemma? Jerry -- Engineering is the art of making what you want from things you can get. ¿¿¿¿¿ ¿¿¿[OS lash]¿¿¿¿[DownQuest ion]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? Originator: rhn@mauve.rahul.net (Ronald H. Nicholson Jr.) >You can't sample rainfall at all because at any instant there's either a >drop or there isn't, and sampling is about what happens at instants. >When a drop hits, the derivative is, at the very least, very large, and >between drops, it is zero. So sampling the derivative isn't much use. On any of the visual rain gauge I've used, a single rain drop would not register above measurement error (noise). Fortunately, a rain gauge is an integrator, so one can just wait long enough to see about how long it takes for the change in measurement to become perceptible, and then use the reciprocal to get the derivative within your measurement error bounds. The derivative is quite important in terms of choice of clothing and/or rain gear. An inch of downpour in 10 minutes will have quite a different effect on ones comfort outdoors compared an inch of sprinkles spread roughly evenly over 24 hours (other environmental conditions being equal). Due to evaporation effects and the possibility of damage to blossoms, this rate makes a difference to farmers as well. Stock price reports are weird because they usually report the closing price, instead of the daily or running average. There's no integration or low pass filter on the number stream (other than that indirectly caused by human nature and trading strategies). IMHO. YMMV. -- Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/ #include // only my own opinions, etc. === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? >You can't sample rainfall at all because at any instant there's ... >drop or there isn't, and sampling is about what happens at insta... >When a drop hits, the derivative is, at the very least, very lar... >between drops, it is zero. So sampling the derivative isn't much... > On any of the visual rain gauge I've used, a single rain drop wou... > register above measurement error (noise). Fortunately, a rain ga... > an integrator, so one can just wait long enough to see about how ... > it takes for the change in measurement to become perceptible, and... > use the reciprocal to get the derivative within your measurement ... > bounds. > The derivative is quite important in terms of choice of clothing ... > rain gear. An inch of downpour in 10 minutes will have quite a d... > effect on ones comfort outdoors compared an inch of sprinkles spr... > roughly evenly over 24 hours (other environmental conditions bein... > equal). Due to evaporation effects and the possibility of damage... > blossoms, this rate makes a difference to farmers as well. A look into the methods of measuring rainfall I think would be appropriate here. Often what's used, in a situation where rainfall is to be monitored automatically, is what's called a tip bucket rain guage. This device outputs a pulse train or triggers a contact closure every time a fixed, yet small, amount of rainfall occurs. A small vessel is split in two and is fixed atop a hinge of sorts. When enough rain enters one half to cause it to tip over, a switch closure event happens and that side is emptied as the opposite side begins to fill. Repeating events can be logged (with time, date) or multiple events can be counted and the total logged on a periodic basis (sampling) either with or without a reset. Rainfall rate can be determined from the count reached between samples and rainfall total over the course of a day, week, or month can be easily determined from a running total. No need for instantaneous samples or trying to measure visual rainfall guages (or individual drops!). The limiting factor is how small of an event you'd like to measure. If your bucket doesn't tip, the water either evaporates and is not recorded or is carried forward to the next event, skewing results there. (You could attempt to model or correct for this, adding a half bucket to each event where little rain and hot weather follows (or low RH%), and or where cool weather and little time separated two events.) The rate resolution you'd like determines your sampling period. Better may be to record each closure and sample (time divide) however you'd like later. This would reduce data set size and allow for flexibility later, however some data preparation may be required. Any significant rainfalls though may actually increase data set size beyond periodic sampling of counts. Your approach should take into account a decent appraisal of expected rain events, the capabilities of your data storage device, and how often you can retrieve collected data. My recommendation would be to setup your datalogger to timestamp and record non-zero counts every two minutes, resetting the counter each time. Adjust to taste. If you require a large dynamic range perhaps log a large and a small set of buckets - small for sensitivity and large to reduce the chance of saturation and missing drops due to splashing during a heavy event. Discount the large bucket (don't add it!) if the rate wasn't especially high. Factor it in if the large and small bucket data doesn't match. Quantized, pseudo-integrated rain data? Hope this helps. -- @ Ag. Engineering Help? @ Random Advice? @ questions __ 80d ___ org === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? >>You can't sample rainfall at all because at any instant there's either a >>drop or there isn't, and sampling is about what happens at instants. >>When a drop hits, the derivative is, at the very least, very large, and >>between drops, it is zero. So sampling the derivative isn't much use. > On any of the visual rain gauge I've used, a single rain drop would not > register above measurement error (noise). Fortunately, a rain gauge is > an integrator, so one can just wait long enough to see about how long > it takes for the change in measurement to become perceptible, and then > use the reciprocal to get the derivative within your measurement error > bounds. > The derivative is quite important in terms of choice of clothing and/or > rain gear. An inch of downpour in 10 minutes will have quite a different > effect on ones comfort outdoors compared an inch of sprinkles spread > roughly evenly over 24 hours (other environmental conditions being > equal). Due to evaporation effects and the possibility of damage to > blossoms, this rate makes a difference to farmers as well. > Stock price reports are weird because they usually report the closing > price, instead of the daily or running average. There's no integration > or low pass filter on the number stream (other than that indirectly > caused by human nature and trading strategies). > IMHO. YMMV. The OP was trying to treat rainfall as a continuous function with measurable derivatives of all orders. My ridiculous counter example was intended to remind him that not every theory of measurement can be applied to every measurement. You know better, so my scenario wasn't intended for you (or others who also don't need to be reminded). The weather bureau's reporting of average temperatures is also weird. The report not the integrated average, but the arithmetic mean of high and low. So a that starts with 30 degrees and rising at midnight, reaches a high of 60 before noon and stays around there until dark, falling to 45 by midnight has an average temperature of 40 degrees. A day that starts at 40, drops to 30 by morning, rises slightly to 35 by noon, briefly reaches 60 by late afternoon, then quickly descends, reaching 30 again by midnight, has the same average. Both stock prices and daily average temperatures are sampled once daily. Can they be considered to be bandlimited to 1/2 cycle per day, or are they aliased? How would aliasing be manifest? Jerry -- Engineering is the art of making what you want from things you can get. ¿¿¿¿¿ ¿¿¿[OS lash]¿¿¿¿[DownQuest ion]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? <33e3juF3ubvk8U1@individual.net> windows-nt) > [...] > Both stock prices and daily average temperatures are sampled once daily. > Can they be considered to be bandlimited to 1/2 cycle per day, or are > they aliased? How would aliasing be manifest? Hey Jerry, that's an interesting question that I've asked myself. In other words, if you were doing DSP on the stock market, how fast would your price sample rate have to be? I would imagine that, if you undersampled, you'd have the same problem as with any signal - an erroneous (aliased) signal. If money were no object, how fast of a feed can one get on stock prices? What's the latency? You can look at an on-line stock purchase system as a sort of feedback system so I'd imagine delay is important just as for any feedback system. Reuters has some info here http://about.reuters.com/productinfo/equities/?seg=3 -- % Randy Yates % So now it's getting late, %% Fuquay-Varina, NC % and those who hesitate %%% 919-577-9882 % got no one... %%%% % 'Waterfall', *Face The Music*, ELO http://home.earthlink.net/~yatescr === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > Both stock prices and daily average temperatures are sampled once daily. > Can they be considered to be bandlimited to 1/2 cycle per day, or are > they aliased? How would aliasing be manifest? > Jerry By the presence or lack thereof of freezer-burned and cooked stockbrokers lying broken on the sidewalks of your local financial district? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: do you have a simple way of roughly estimate the max frequency?how about this interpolation scheme? > You can't sample rainfall at all because at any instant there's either a > drop or there isn't, and sampling is about what happens at instants. I would disagree. When a farmer wants to know how much rainfall there has been in order to decide how much irrigation his crops will require he has a perfectly good bandlimited continuous function called 'rainfall' which he can refer to. And it is indeed a function that is sampled at instants (points in both time and space) even though the sampling device may spend all 24/7 collecting data. Also, it is a very accurate representation of the moisture that is getting to the roots of his crops which is what the farmer means when he says 'rainfall'. > When a drop hits, the derivative is, at the very least, very large, and > between drops, it is zero. So sampling the derivative isn't much use. 2 rain gauges set a foot apart in the open will have no discernible difference in their readings so there is no need to measure individual raindrops. The diameter of the rain gauge (within reason) has no effect on the measurement of the rainfall function - the function just simply isn't changing fast enough. What you or the OP mean by measuring the derivatives of rainfall I have no clue. -jim > OK: lets get real. What we really do ... > Wait: you tell me. How do you propose to collect your samples? What > limitations do that sampling scheme impose? When you respect those > limitations, is there still a dilemma? > Jerry > -- > Engineering is the art of making what you want from things you can get. > ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ http://www.newsfeeds.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= East/West-Coast Server Farms - Total Privacy via Encryption =--- === Subject: Re: do you have a simple way of roughly estimate the max frequency?how about this interpolation scheme? >>You can't sample rainfall at all because at any instant there's either a >>drop or there isn't, and sampling is about what happens at instants. > I would disagree. When a farmer wants to know how much rainfall there > has been in order to decide how much irrigation his crops will require > he has a perfectly good bandlimited continuous function called > 'rainfall' which he can refer to. And it is indeed a function that is > sampled at instants (points in both time and space) even though the > sampling device may spend all 24/7 collecting data. Also, it is a very > accurate representation of the moisture that is getting to the roots of > his crops which is what the farmer means when he says 'rainfall'. He doesn't sample the rate of fall at an instant in time. Instead, he checks his rain gauge for accumulated rainfall. He is rarely interested in rate, and when he is, he settles for an average rate over some (probably variable) time. >>When a drop hits, the derivative is, at the very least, very large, and >>between drops, it is zero. So sampling the derivative isn't much use. > 2 rain gauges set a foot apart in the open will have no discernible > difference in their readings so there is no need to measure individual > raindrops. The diameter of the rain gauge (within reason) has no effect > on the measurement of the rainfall function - the function just simply > isn't changing fast enough. > What you or the OP mean by measuring the derivatives of rainfall I have > no clue. In most places, an inch an hour is considered heavy rain, but it frequently rains at that heavy rate for brief periods. Once, when it had already rained copiously during much of the day, we had a total additional rainfall of 4 inches in a little under an hour. Children used inflatable wading pools to raft down our main street. The manhole cover at it low point had been pushed aside by the water pressure and a geyser of much diluted sewage spewed 12 feet into the air. Although usually only the total matters, sometimes rate matters too. The OP's error was treating rainfall as a bandlimited periodic function. I was trying to get him to think instead of just pushing variables around. Similar problems arise when sampling stock prices. ... Jerry -- Engineering is the art of making what you want from things you can get. ¿¿¿¿¿ ¿¿¿[OS lash]¿¿¿¿[DownQuest ion]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? > The OP's error was treating rainfall as a bandlimited periodic function. Your error is you have said nothing to support this claim. If the farmers fields are flat his definition of rainfall is in fact a bandlimited periodic function and he's not to terribly interested in what effect it has on your pavement covered environment. If your interested in examining rainfall on a cyclic period of 5 to 10 days it doesn't much matter whether you collect data religiously once an hour or once a day your conclusions based on the data on whether to irrigate (to artificially maintain the optimal periodic cycle) will be the same. -jim > I was trying to get him to think instead of just pushing variables > around. Similar problems arise when sampling stock prices. > ... > Jerry > -- > Engineering is the art of making what you want from things you can get. > ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ http://www.newsfeeds.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= East/West-Coast Server Farms - Total Privacy via Encryption =--- === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? Can you stop re-arranging the letters and spacings in the subject line of these posts. It's a little disorientating to have a thread breaking off into several permutations within the group It's makes a mess in Google as well. >> The OP's error was treating rainfall as a bandlimited periodic function. >Your error is you have said nothing to support this claim. If the >farmers fields are flat his definition of rainfall is in fact a >bandlimited periodic function and he's not to terribly interested in >what effect it has on your pavement covered environment. > If your interested in examining rainfall on a cyclic period of 5 to 10 >days it doesn't much matter whether you collect data religiously once an >hour or once a day your conclusions based on the data on whether to >irrigate (to artificially maintain the optimal periodic cycle) will be >the same. >-jim >> I was trying to get him to think instead of just pushing variables >> around. Similar problems arise when sampling stock prices. >> ... >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ >http://www.newsfeeds.com The #1 Newsgroup Service in the World! >100,000 Newsgroups >---= East/West-Coast Server Farms - Total Privacy via Encryption =--- ( modify address for return mail ) www.numbersusa.com www.americanpatrol.com === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? > Can you stop re-arranging the letters and spacings in the subject line > of these posts. No I'm afraid I can't since I have never done that. Your posting appears in my newsreader in response to my posting with the same subject line as all other posts above it in this thread. What is your newsreader showing? -jim http://www.newsfeeds.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= East/West-Coast Server Farms - Total Privacy via Encryption =--- === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? >> Can you stop re-arranging the letters and spacings in the subject line >> of these posts. >No I'm afraid I can't since I have never done that. Your posting appears >in my newsreader in response to my posting with the same subject line as >all other posts above it in this thread. What is your newsreader >showing? With Agent, I am seeing 5 different threads for this topic. 1) An original thread, with the 13 posts prior to your first reply, contained under the heading: === Subject: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? 2) Your 1st reply, by itself, under the heading: === Subject: Re: do you have a simple way of roughly estimate the max frequency?how about this interpolation scheme? With it, there are now 3 characters between how and about, instead of 1. It might be that some or all of those extra characters are associated with a line return that was inserted. 3) Jerry's reply, by itself with: === Subject: Re: do you have a simple way of roughly estimate the max frequency?how about this interpolation scheme? Now there are 5 characters between how and about 4) Your 2nd reply, by itself with: === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? Where there are 3 characters between max and frequency, but none between how and about. 5) This, your 3rd reply, by itself with: === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? Where there are 4 characters been max and frequency, and none between how and about. heading, it has inserted a new subheading after some of the changes listed above ... so it is seeing differences as well. I also glanced at your previous posts to comp.dsp, and some of them stay in the same single parent thread, and some break off like this. The ones that break off have extra long subject headers like this topic, so maybe that is causing trouble. Robert ( modify address for return mail ) www.numbersusa.com www.americanpatrol.com === Subject: Re: do you have a simple way of roughly estimate the max frequency?howabout this interpolation scheme? >Can you stop re-arranging the letters and spacings in the subject line >of these posts. >>No I'm afraid I can't since I have never done that. Your posting appears >>in my newsreader in response to my posting with the same subject line as >>all other posts above it in this thread. What is your newsreader >>showing? > With Agent, I am seeing 5 different threads for this topic. > 1) An original thread, with the 13 posts prior to your first reply, contained > under the heading: === > Subject: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > 2) Your 1st reply, by itself, under the heading: === > Subject: Re: do you have a simple way of roughly estimate the max frequency?how > about this interpolation scheme? > With it, there are now 3 characters between how and about, instead of 1. It might be > that some or all of those extra characters are associated with a line return that was inserted. > 3) Jerry's reply, by itself with: === > Subject: Re: do you have a simple way of roughly estimate the max frequency?how > about this interpolation scheme? > Now there are 5 characters between how and about > 4) Your 2nd reply, by itself with: === > Subject: Re: do you have a simple way of roughly estimate the max > frequency?howabout this interpolation scheme? > Where there are 3 characters between max and frequency, but none between how and > about. > 5) This, your 3rd reply, by itself with: === > Subject: Re: do you have a simple way of roughly estimate the max > frequency?howabout this interpolation scheme? > Where there are 4 characters been max and frequency, and none between how and > about. > heading, it has inserted a new subheading after some of the changes listed above ... so it is > seeing differences as well. > I also glanced at your previous posts to comp.dsp, and some of them stay in the same single > parent thread, and some break off like this. The ones that break off have extra long subject > headers like this topic, so maybe that is causing trouble. > Robert > ( modify address for return mail ) > www.numbersusa.com > www.americanpatrol.com I sometimes see missing spaces between words and long runs of spaces between runs in posts of my own. Most others don't see than. Newsreaders don't always operate as what you see is what is there any more. Line wrap is a documented and intentional example. Jerry -- Engineering is the art of making what you want from things you can get. ¿¿¿¿¿ ¿¿¿[OS lash]¿¿¿¿[DownQuest ion]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿¿¿ ¿¿¿[OSl ash]¿¿¿¿[DownQuesti on]¿¿¿ ¿¿¿ === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > Hi all, > Do you have a simple way of roughly estimate the max freuqency in a plot > of data? Double the rciprocal of the mean time between observations is a reasonable figure to use. Franz === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? >> Hi all, >> Do you have a simple way of roughly estimate the max freuqency in > a plot >> of data? > Double the rciprocal of the mean time between observations is a > reasonable figure to use. > Franz ???? If an observation is a sample then how does this address the concern? Fred === Subject: Re: do you have a simple way of roughly estimate the max frequency? how about this interpolation scheme? > Hi all, > Do you have a simple way of roughly estimate the max freuqency in a plot > of data? > For example, suppse I have collect a trace of data about one week's raining > amount... I have to decide how much is the Nyquist sampling rate and how > many samples do I need... how do I estimate the max frequency in the > rainning data roughly? > If I used Matlab to do data spectrum plot of the past a few years and find > the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist > rate to be 2 cycle per day, i.e. I measure twice data a day... of the > function x(t)... > But now I want to measure once a day, but sampling both x(t) and x'(t) > (derivitative) once per day... for what kind of x(t) can I do this kind of > lazy measurement sampling? it is less than Nyquist, so you have distorted data > How do I reconstruct the original function x(t) by having the x(t) and x'(t) > samples for one measurement per day? > Can I reduce the measurements to once per week, by sampling x(t), x'(t) , > x''(t), ... till the 14th derivative? > What are the reasons why this sampling/interpolation scheme has not been > used in practice? Think of it, using only one sample per week, you can predict the rain amouts for each day? hardly. derivitatives bring up noise, by the second/third your data is all noise a derivitative is a high pass filter > Any ideas? === Subject: any successful stories of gambling using those math/stat theorems? Hi all, I recently learned a lot about gambler's ruin, random walks, and gambling problems... I am wondering if these maths are really useful in Las Vegas and casinos... Can anybody telll some successful stories of gambling using math/stat as tools? I really need some motivation of learning deeper maths/stat about these gambling theories... === Subject: Re: any successful stories of gambling using those math/stat theorems? My study of probability theory has kept me from gambling, period, so I would say math has made me a successful gambler. For an interesting read about one of the first card-counters in Blackjack who went public try _Beat the Dealer_ by Edward O. Thorp. It explains the system and also tells stories of what the casinos did in response to Thorp's winning large amounts. === Subject: Re: any successful stories of gambling using those math/stat theorems? > Hi all, > I recently learned a lot about gambler's ruin, random walks, and gambling > problems... I am wondering if these maths are really useful in Las Vegas and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... Work out side bets with the players that are more favorable to you than the odds at the tables. === Subject: Re: any successful stories of gambling using those math/stat theorems? >Hi all, >I recently learned a lot about gambler's ruin, random walks, and gambling >problems... I am wondering if these maths are really useful in Las Vegas and >casinos... Can anybody telll some successful stories of gambling using >math/stat as tools? I really need some motivation of learning deeper >maths/stat about these gambling theories... Card counting and Kelly Betting seem to be the most rational applications of well defined math to gambling. http://www.ehow.com/how_4369_count-cards.html http://www.bjmath.com/bjmath/kelly/kelly.htm I believe enough in Kelly Betting that I applied it to the problem of deciding how much investment should be in stocks and how much in fixed income securities. http://home.rochester.rr.com/jbxroads/kelly/ This worked great through the recent market collapse. Based on your question, I looked for results from Kelly Betting using a Google search. The ratio of results available to papers on how to do it are rather slim. My favorite success story is Doan Farmer's. AISTR, while at university he and two others made a run on the casinos. Farmer went on to fame and fortune but also sold a screenplay about his teams success in Las Vegas. In an earlier time it was listed on his cv at the Santa Fe Institute. http://www.santafe.edu/~jdf/ John Bailey http://home.rochester.rr.com/jbxroads/mailto.html === Subject: Re: any successful stories of gambling using those math/stat theorems? >>Hi all, >>I recently learned a lot about gambler's ruin, random walks, and gambling >>problems... I am wondering if these maths are really useful in Las Vegas >>and >>casinos... Can anybody telll some successful stories of gambling using >>math/stat as tools? I really need some motivation of learning deeper >>maths/stat about these gambling theories... > Card counting and Kelly Betting seem to be the most rational > applications of well defined math to gambling. > http://www.ehow.com/how_4369_count-cards.html > http://www.bjmath.com/bjmath/kelly/kelly.htm > I believe enough in Kelly Betting that I applied it to the problem of > deciding how much investment should be in stocks and how much in fixed > income securities. > http://home.rochester.rr.com/jbxroads/kelly/ > This worked great through the recent market collapse. > Based on your question, I looked for results from Kelly Betting using > a Google search. The ratio of results available to papers on how to > do it are rather slim. > My favorite success story is Doan Farmer's. AISTR, while at > university he and two others made a run on the casinos. Farmer went > on to fame and fortune but also sold a screenplay about his teams > success in Las Vegas. In an earlier time it was listed on his cv at > the Santa Fe Institute. http://www.santafe.edu/~jdf/ > John Bailey > http://home.rochester.rr.com/jbxroads/mailto.html So if I apply the card-counting to blackjack, I will be arrested in Las Vegas, But I won't have trouble on online casinos, right? === Subject: Re: any successful stories of gambling using those math/stat theorems? > Hi all, > I recently learned a lot about gambler's ruin, random walks, and gambling > problems... I am wondering if these maths are really useful in Las Vegas and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... In the book _Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise_ by Manfred Robert Schroeder, the author mentions a system for beating roulette based on probability, the laws of motion, and a small, special purpose computer. IMO the book is a very good read for that story and many other interesting topics it presents. Russell -- All too often the study of data requires care. === Subject: Re: any successful stories of gambling using those math/stat theorems? Open your own Casino and/or a Lottery. kiki: > I recently learned a lot about gambler's ruin, random walks, and > gambling problems... I am wondering if these maths are really useful > in Las Vegas and casinos... Can anybody telll some successful > stories of gambling using math/stat as tools? I really need some > motivation of learning deeper maths/stat about these gambling > theories... === Subject: Re: any successful stories of gambling using those math/stat theorems? agreed, that's probably the only way you are 'mathematically guranteed' to succeed in this line of work. === Subject: Re: any successful stories of gambling using those math/stat theorems? > Hi all, > I recently learned a lot about gambler's ruin, random walks, and gambling > problems... I am wondering if these maths are really useful in Las Vegas and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... Yes, All of the games have probabilities calculated out and the odds are know by the casino. You can calculate them out to with math/stat/prob. but you can't change the game. You can't really determine winning numbers. You can determine which game has better payout with probability. (all these lose money in the long run) Blackjack - good Roulette - odds are poor and so on === Subject: Re: any successful stories of gambling using those math/stat theorems? >> Hi all, >> I recently learned a lot about gambler's ruin, random walks, and gambling >> problems... I am wondering if these maths are really useful in Las Vegas >and >> casinos... Can anybody telll some successful stories of gambling using >> math/stat as tools? I really need some motivation of learning deeper >> maths/stat about these gambling theories... >Yes, All of the games have probabilities calculated out and the odds are >know by the casino. >You can calculate them out to with math/stat/prob. but you can't change the >game. >You can't really determine winning numbers. >You can determine which game has better payout with probability. > (all these lose money in the long run) >Blackjack - good >Roulette - odds are poor >and so on Card counting works with blackjack Craps is a matter of knowing when to bet and when not Roulette although it has poor odds is the only game where a group of mathematicians went in and broke the bank. It seems that they were able to calculate which numbers came up more often because the wheel is never 100% balanced. The story is rather famous I believe. Leslie 'Mack' McBride remove text between _ marks to respond via e-mail === Subject: Re: any successful stories of gambling using those math/stat theorems? > Hi all, > I recently learned a lot about gambler's ruin, random walks, and > gambling > problems... I am wondering if these maths are really useful in Las Vegas >>and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... >>Yes, All of the games have probabilities calculated out and the odds are >>know by the casino. >>You can calculate them out to with math/stat/prob. but you can't change >>the >>game. >>You can't really determine winning numbers. >>You can determine which game has better payout with probability. >> (all these lose money in the long run) >>Blackjack - good >>Roulette - odds are poor >>and so on > Card counting works with blackjack > Craps is a matter of knowing when to bet and when not > Roulette although it has poor odds is the only game where > a group of mathematicians went in and broke the bank. It seems > that they were able to calculate which numbers came up more often > because the wheel is never 100% balanced. The story is rather > famous I believe. > Leslie 'Mack' McBride > remove text between _ marks to respond via e-mail That's great! Do you know the algorithm how they defeat the roulette and is that technique still applicable? === Subject: Re: any successful stories of gambling using those math/stat theorems? > Hi all, > I recently learned a lot about gambler's ruin, random walks, and gambling > problems... I am wondering if these maths are really useful in Las Vegas >>and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... >>You can determine which game has better payout with probability. >> (all these lose money in the long run) >>Blackjack - good >>Roulette - odds are poor >Card counting works with blackjack Only if the house doesn't shuffle the deck(s) prior to you acting on the count. Not a very likely scenario, today. >Craps is a matter of knowing when to bet and when not In my experience this is quite true. Best strategy I've found: never bet! >Roulette although it has poor odds is the only game where >a group of mathematicians went in and broke the bank. In Nevada, they would risk detention, by the casino, under NRS xx.xx for suspicion of cheating. Not a good time, most likely followed by free trip to Carson City.... Rich === Subject: Re: any successful stories of gambling using those math/stat theorems? >> Hi all, >> >> I recently learned a lot about gambler's ruin, random walks, and >> gambling >> problems... I am wondering if these maths are really useful in Las >> Vegas >and >> casinos... Can anybody telll some successful stories of gambling using >> math/stat as tools? I really need some motivation of learning deeper >> maths/stat about these gambling theories... >> >> >You can determine which game has better payout with probability. > (all these lose money in the long run) >Blackjack - good >Roulette - odds are poor >>Card counting works with blackjack > Only if the house doesn't shuffle the deck(s) prior to you acting on the > count. > Not a very likely scenario, today. >>Craps is a matter of knowing when to bet and when not > In my experience this is quite true. Best strategy I've found: never bet! >>Roulette although it has poor odds is the only game where >>a group of mathematicians went in and broke the bank. > In Nevada, they would risk detention, by the casino, under NRS xx.xx for > suspicion of cheating. Not a good time, most likely followed by free trip > to > Carson City.... > Rich Carson City, you mean prison? that's bad... maybe some other places over the world ? === Subject: Re: any successful stories of gambling using those math/stat theorems? >> Hi all, >> >> I recently learned a lot about gambler's ruin, random walks, and gambling >> problems... I am wondering if these maths are really useful in Las Vegas >and >> casinos... Can anybody telll some successful stories of gambling using >> math/stat as tools? I really need some motivation of learning deeper >> maths/stat about these gambling theories... >> >> >Yes, All of the games have probabilities calculated out and the odds are >know by the casino. >You can calculate them out to with math/stat/prob. but you can't change the >game. >You can't really determine winning numbers. >You can determine which game has better payout with probability. > (all these lose money in the long run) >Blackjack - good >Roulette - odds are poor >and so on > Card counting works with blackjack Proven true. However, you need to know how to work the system, find a casino that is vulnerable (single deck, wide bet-amount tolerance), and not get thrown out or arrested. > Craps is a matter of knowing when to bet and when not That is true only if you never bet. > Roulette although it has poor odds is the only game where > a group of mathematicians went in and broke the bank. It seems > that they were able to calculate which numbers came up more often > because the wheel is never 100% balanced. The story is rather > famous I believe. It has never been proven to be anything more than a way to sell books. Anyone who thinks a roulette spin can be predicted doesn't understand the variables involved. The legend is probably helped along by stories of crooked wheels and friendly croupiers, as in the movie Casablanca. === Subject: Re: any successful stories of gambling using those math/stat theorems? >> > Hi all, > > I recently learned a lot about gambler's ruin, random walks, and >gambling > problems... I am wondering if these maths are really useful in Las >Vegas >>and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... > > >> >>Yes, All of the games have probabilities calculated out and the odds are >>know by the casino. >>You can calculate them out to with math/stat/prob. but you can't change >the >>game. >>You can't really determine winning numbers. >>You can determine which game has better payout with probability. >> (all these lose money in the long run) >>Blackjack - good >>Roulette - odds are poor >>and so on >> >> Card counting works with blackjack >Proven true. However, you need to know how to work the system, find a >casino that is vulnerable (single deck, wide bet-amount tolerance), and not >get thrown out or arrested. >> Craps is a matter of knowing when to bet and when not >That is true only if you never bet. Some bets pay decent odds giving you a better chance of winning ... others are sucker bets. Playing on-line removes any skill a dice thrower might have as well as having absolutely balanced dice. Real dice are seldom absolutely balanced. >> Roulette although it has poor odds is the only game where >> a group of mathematicians went in and broke the bank. It seems >> that they were able to calculate which numbers came up more often >> because the wheel is never 100% balanced. The story is rather >> famous I believe. >It has never been proven to be anything more than a way to sell books. >Anyone who thinks a roulette spin can be predicted doesn't understand the >variables involved. The legend is probably helped along by stories of >crooked wheels and friendly croupiers, as in the movie Casablanca. There are a lot of variables involved. The group that did this (in europe) spent some time analyzing one particular wheel. A variance of 4% is sufficient to turn roulette into a winning game at odds of 35:1. American roulette wheels have an extra space giving the house an added advantage. An on-line roulette wheel is guaranteed to be balanced so there is no advantage the same is not true of a mechanical wheel. Leslie 'Mack' McBride remove text between _ marks to respond via e-mail === Subject: Re: any successful stories of gambling using those math/stat theorems? >> Craps is a matter of knowing when to bet and when not >That is true only if you never bet. > Some bets pay decent odds giving you a better chance of winning ... > others are sucker bets. Playing on-line removes any skill a dice > thrower might have as well as having absolutely balanced dice. Real > dice are seldom absolutely balanced. All bets allowed on the table are guaranteed to pay something to the house, in the long run. I admit that some bets have better odds for the house than others. However, unless you accept the entertainment or comp value of the game to be sufficient to offset the house advantage, all craps bets are sucker bets. === Subject: Re: any successful stories of gambling using those math/stat theorems? >> > Craps is a matter of knowing when to bet and when not >> >>That is true only if you never bet. >> Some bets pay decent odds giving you a better chance of winning ... >> others are sucker bets. Playing on-line removes any skill a dice >> thrower might have as well as having absolutely balanced dice. Real >> dice are seldom absolutely balanced. >All bets allowed on the table are guaranteed to pay something to the house, >in the long run. I admit that some bets have better odds for the house than >others. However, unless you accept the entertainment or comp value of the >game to be sufficient to offset the house advantage, all craps bets are >sucker bets. Agreed the house always has some advantage in craps with perfect dice. Dice, however, aren't perfect. Since the house odds are only about 1.5% a hot pair of dice can offer a significant advantage. Shooters will ask for cold dice to be replaced. However the house will replace a pair of dice that seems to be hot if a significant amount of money is won. 24 rolls (usually about 5 shooters) are all that are required to determine if the dice are rolling true. Of course you have to be able to do statistics in your head, no computers allowed. The casinos routinely do the same thing and pulls dice with significant statistical abnormalities if they are losing money. Of course they get to use computers. Craps is a nice way of testing a random number generator. In this case a physical one. Leslie 'Mack' McBride remove text between _ marks to respond via e-mail === Subject: Re: any successful stories of gambling using those math/stat theorems? > An on-line roulette wheel is guaranteed to be balanced so there is > no advantage the same is not true of a mechanical wheel. I wouldn't be surprised if there were online casinos with unbalanced wheels, weighted in favour of the house. It would be a pretty trivial programming task to look at the current bets for a given spin, and adjust the probabilities enough to make a difference in the long term but not enough to be detectable in the short-medium term. Of course the house already has a guaranteed long-run advantage for an unweighted wheel, so they'd have to be pretty greedy. - Tim === Subject: Re: any successful stories of gambling using those math/stat theorems? >> > Hi all, > > I recently learned a lot about gambler's ruin, random walks, and > gambling > problems... I am wondering if these maths are really useful in Las > Vegas >>and > casinos... Can anybody telll some successful stories of gambling using > math/stat as tools? I really need some motivation of learning deeper > maths/stat about these gambling theories... > > >> >>Yes, All of the games have probabilities calculated out and the odds are >>know by the casino. >>You can calculate them out to with math/stat/prob. but you can't change > the >>game. >>You can't really determine winning numbers. >>You can determine which game has better payout with probability. >> (all these lose money in the long run) >>Blackjack - good >>Roulette - odds are poor >>and so on >> >> Card counting works with blackjack > Proven true. However, you need to know how to work the system, find a > casino that is vulnerable (single deck, wide bet-amount tolerance), and > not > get thrown out or arrested. >> Craps is a matter of knowing when to bet and when not > That is true only if you never bet. >> Roulette although it has poor odds is the only game where >> a group of mathematicians went in and broke the bank. It seems >> that they were able to calculate which numbers came up more often >> because the wheel is never 100% balanced. The story is rather >> famous I believe. > It has never been proven to be anything more than a way to sell books. > Anyone who thinks a roulette spin can be predicted doesn't understand the > variables involved. The legend is probably helped along by stories of > crooked wheels and friendly croupiers, as in the movie Casablanca. By doing math to help win I will get arrested? === Subject: Re: any successful stories of gambling using those math/stat theorems? > By doing math to help win I will get arrested? It is illegal to use any mechanical, electric, or calculating device to assist you. Even if you do it all in your head, it is illegal to count cards. Nice business, that casino business, eh? === Subject: Re: any successful stories of gambling using those math/stat theorems? <5dOzd.4597$yW5.3477@fed1read02> > By doing math to help win I will get arrested? > It is illegal to use any mechanical, electric, or calculating device to > assist you. Even if you do it all in your head, it is illegal to count > cards. False. The illegality of card-counting is disinformation spread by the casinos. They have every right to not allow you to play, however, and they will usually share information with other casinos. === Subject: Re: any successful stories of gambling using those math/stat theorems? > By doing math to help win I will get arrested? > It is illegal to use any mechanical, electric, or calculating device to > assist you. Even if you do it all in your head, it is illegal to count > cards. How is anyone going to prove what you're doing in your head? > Nice business, that casino business, eh? For everyone but Donald Trump! === Subject: Re: any successful stories of gambling using those math/stat theorems? > By doing math to help win I will get arrested? > It is illegal to use any mechanical, electric, or calculating device to > assist you. Even if you do it all in your head, it is illegal to count > cards. > How is anyone going to prove what you're doing in your head? If you change the amounts of your bets dramatically from time to time (for example, from the table low limit to the table high limit), and are making money, you will be asked to play somewhere else. If you come back to the same casino later, you will be recognized and given a more severe warning. Of course, you can just move over to the slots or craps or roulette tables, and everyone will be smiling. === Subject: Re: any successful stories of gambling using those math/stat theorems? >> By doing math to help win I will get arrested? >> >> It is illegal to use any mechanical, electric, or calculating device to >> assist you. Even if you do it all in your head, it is illegal to count >> cards. >> How is anyone going to prove what you're doing in your head? >If you change the amounts of your bets dramatically from time to time (for >example, from the table low limit to the table high limit), and are making >money, you will be asked to play somewhere else. If you come back to the >same casino later, you will be recognized and given a more severe warning. The more severe warning involves handcuffs. If you are asked to leave and come back they call that trespassing. >Of course, you can just move over to the slots or craps or roulette tables, >and everyone will be smiling. Leslie 'Mack' McBride remove text between _ marks to respond via e-mail === Subject: how to pass a random process through a non-linear system? Hi all, I understood how to pass a stationary random process through a LTI syste... the autocorrelation of the output has a beautiful relation with the input's autocorrelations, and so does the power spectrum density... But what if my stationary zero mean Gaussian random process x(t) go through a non-linear system, for example, a signum device(output 1 for input x(t)>0 and output -1 for input x(t)<=0)) How to find the autocorrelation and the power spectrum density of the output if I was given an input autocorrelation? === Subject: Re: how to pass a random process through a non-linear system? > Hi all, > I understood how to pass a stationary random process through a LTI syste... > the autocorrelation of the output has a beautiful relation with the input's > autocorrelations, and so does the power spectrum density... > But what if my stationary zero mean Gaussian random process x(t) go through > a non-linear system, for example, a signum device(output 1 for input x(t)>0 > and output -1 for input x(t)<=0)) > How to find the autocorrelation and the power spectrum density of the output > if I was given an input autocorrelation? In general this is not an easy problem. In the case you have presented, however, there is a solution. The solution I have comes from Lawson and Uhlenbeck, Threshold Signals, MIT Radiation Laboratory Series, McGraw-Hill, 1950, page 57. They reference an earlier Radiation Lab Report (Van Vleck, The Spectrum of Clipped Noise, RRL Report 51, July 21, 1943), which you can purchase from the MIT library, last I checked. It's not cheap. Van Vleck's work was also published in the IEEE Proceedings a few years ago (1966?), with Middleton as a coauthor. The final result is Ry(t) = (2/pi)asin(Rx(t)/Rx(0)), where Ry is the output autocorrelation, and Rx is the input autocorrelation. The power spectrum of the noise is the Fourier Transform of Ry(t), which is often easy to calculate using numerical math packages. Note that if your input is not band-limited, then Rx(t)/Rx(0) = 1 when t = 0, and 0 elsewhere, making the Fourier Transform easy to calculate. -- Mike -- === Subject: Re: how to pass a random process through a non-linear system? > Hi all, > I understood how to pass a stationary random process through a LTI syste... > the autocorrelation of the output has a beautiful relation with the input's > autocorrelations, and so does the power spectrum density... > But what if my stationary zero mean Gaussian random process x(t) go through > a non-linear system, for example, a signum device(output 1 for input x(t)>0 > and output -1 for input x(t)<=0)) > How to find the autocorrelation and the power spectrum density of the output > if I was given an input autocorrelation? Yes I believe this has been done by Wiener. I think it is called the Wiener expansion and such work has been done by others independently eg Barrett back in the 1940s! It will take you quite a while to track down the refs but most of it is there. Country Chiel === Subject: Re: how to pass a random process through a non-linear system? > Hi all, > I understood how to pass a stationary random process through a LTI syste... > the autocorrelation of the output has a beautiful relation with the input's > autocorrelations, and so does the power spectrum density... > But what if my stationary zero mean Gaussian random process x(t) go through > a non-linear system, for example, a signum device(output 1 for input x(t)>0 > and output -1 for input x(t)<=0)) > How to find the autocorrelation and the power spectrum density of the output > if I was given an input autocorrelation? If you have a stationary process with known distribution and autocorrelation, then you know: a: the probability distribution of the process at any point in time (this is also the case if you have a non-stationary process with a known time dependence). b: the conditional probability distribution of the process at any point in time given a sample of the process at some other point in time. If you have the above two bits of information and you pass the process through a memoryless nonlinearity (such as your signum function), then you should be able to extract: c: The probability distribution of the process at any point in time. d: The conditional probability distribution of the process at any point in time given a sample of the process at some other point in time. If you know (c) then you can specify whether your output process is stationary (it will be for a stationary input process -- it may not necessarily be for a non-stationary input, depending on the nature of the time dependence and your nonlinearity, I just don't know in general but in specific you should be able to do the math and find out). If you know (d) then you can extract the autocorrelation function. Then you have your answer. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: how to pass a random process through a non-linear system? Use the rules of transformation of random variables to find out the distribution of the output random variable of the non-linear system. Once you have found the distribution, it is a simple job to calculate the autocorrelation function. But if you are only given the input autocorrelation function... i dont think you have enough statistics then to find out the autocorrelation at the output. Wait, a signum device is just a hilbert transformer. So, we know that psd is just the fourier transform of autocorrelation function. Since this being a special case (sorta), i think we can use the convolution property to get the psd and autocorrelation functions at the output. I am just writing down my first thoughts. But hope you can look up literature on hilbert trasforms and figure out the details. Prasanna. === Subject: Re: how to pass a random process through a non-linear system? > Hi all, > I understood how to pass a stationary random process through a LTI syste... > the autocorrelation of the output has a beautiful relation with the input's > autocorrelations, and so does the power spectrum density... > But what if my stationary zero mean Gaussian random process x(t) go through > a non-linear system, for example, a signum device(output 1 for input x(t)>0 > and output -1 for input x(t)<=0)) > How to find the autocorrelation and the power spectrum density of the output > if I was given an input autocorrelation? I don't think you can. === Subject: how to find the level crossing rate? Hi all, I have a stationary random process with zero mean x(t), let's define the level crossing rate to be LCR=lim E{Na(T)}/T as T -> 0... where Na(T) is the number of the level crossings in the time interval T... i.e. the times that the random process x(t) passing through the level x(t)=a... How should I find LCR analytically? It may be difficult... are there any well-known results for simple random processes, such as ON-OFF process, or Gaussian, etc? Any ideas? === Subject: Re: how to find the level crossing rate? > Hi all, > I have a stationary random process with zero mean x(t), let's define the > level crossing rate to be > LCR=lim E{Na(T)}/T as T -> 0... > where Na(T) is the number of the level crossings in the time interval T... > i.e. the times that the random process x(t) passing through the level > x(t)=a... > How should I find LCR analytically? It may be difficult... are there any > well-known results for simple random processes, such as ON-OFF process, or > Gaussian, etc? > Any ideas? Kiki: Ask yourself what the level crossing rate for Gaussian white noise would be. Now try uniformly distributed white noise. Now binary white noise that only occurs at -1 and 1. Now ask yourself if the distribution of the noise is the important characteristic here. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com === Subject: Re: how to find the level crossing rate? > Hi all, > I have a stationary random process with zero mean x(t), let's define the > level crossing rate to be > LCR=lim E{Na(T)}/T as T -> 0... > where Na(T) is the number of the level crossings in the time interval T... > i.e. the times that the random process x(t) passing through the level > x(t)=a... > How should I find LCR analytically? It may be difficult... are there any > well-known results for simple random processes, such as ON-OFF process, or > Gaussian, etc? > Any ideas? It is out there, usually related to a bandwidth. gaussian. I have a book that has it and derived, somewhere, think Microwave is in the title. === Subject: Complex Implicit Functions My website www.riemannsurfaces.info devoted to the above topic is (I hope only temporarily) out of action but the files can be read at http://www.members.lycos.co.uk/conesetter/ other critics who helped me to clarify my ideas and avoid claiming too much. === Subject: Real Analysis: Open set of L^p(0,1) 00Show that L^p(0,1) has no open convex subset between the empty set and >L^p(0,1) itself. Suppose that O is a nonempty convex open set; we can assume that O contains the origin for convenience, since the topology is translation-invariant. Choose delta > 0 so ||f|| < delta implies that f is in O. Suppose that f is in L^p. Fix a large integer N. Split the domain [0,1] into disjoint sets I_1, ... I_N in such a way that if we define f_n(x) = x for x in I_n and 0 otherwise then all the f_n have the same norm. Now f = f_1 + ... + f_N = (g_1 + ... g_N)/N, if g_n = N f_n. So f is a convex combination of the g_n. What is ||g_n||? ************************ David C. Ullrich === Subject: Further Explanation of Pi_sm vs Pi ->( Smart Model Pi = Pi_sm) Smart Model Pi Further explanations... By definition, of a Unit Disk with the smallest possible radius under the conditions shown which relates pi to a spiral using the Golden ratio. The form of the Golden ratio in nested radical form is, phi = sqrt(1 +sqrt(1+sqrt1 + .... sqrt(1)) The form of pi in nest form is, pi = lim 2^n+1 = sqrt(2+sqrt(2+sqrt(2+...+sqrt(2)) Phi in the form of a continued fraction is, Phi = 1 + 1 ------------ 1 + 1 -------- 1 + 1 ------ 1+ ... Phi also has this form, Phi = 1/2 ( 1 + sqrt(5)) = 1.6180339... Phi and Pi have almost identical patterns in wave form analysis, except pi uses sqrt(2) in it's patterns and Phi used sqrt(1) in it's patterns. For a Unit Circle, Unit Circle = 1 The Smart Model Pi is closer related to unity or 1. In the 5 disk problem, the smallest radius that can be formed for a Unit Disk is, 1/Phi = .6180... In the Disk Covering Problem, they use the area that fills in this smallest circle with a symmetrical pattern of circles with a common origin with the smallest circle radius. References http://mathworld.wolfram.com/DiskCoveringProblem.html http://mathworld.wolfram.com/FiveDisksProblem.html I think one of the main difference between Phi and pi is, Phi uses the sqrt(1). Pi uses the sqrt(2). Which looks more accurate? sqrt(1) = 1 or sqrt(2) = 1.41421... The sqrt(1) look more accurate to me for a NEW definition of pi. Phi and Pi almost sound the same. They are very closely related. I think Phi is more accurate in relation to the Fibonacci Spiral. It also uses the Golden Ration. I'm not saying pi doesn't work for something used in the calculating of circles anf spheres, but Pi_sm seems to me to be more accurate in it's relation to a spiral. A good analogous example of Pi_sm is like looking a a CD. The groves look like a circle but if you look closer it's like a very fine compact spiral that forms a circle. If you go to the limits of infinity, this circular spiral looks just like a circle on it's outer edge. With a more precise form of pi, I think more accurate values can be found in nature relative to Pi_sm. Where, Pi_sm = Smart Model Pi The Smart Model uses basically the Helix Spiral Field in it foundations of calculations in the process of Unifing the universe at all levels of analysis from micro to macro. Who appears to be more accurate in nature and life? In nature things appear in spiral form like for example plants and flowers, and even you. You hand itself is related to the Golden Ratio which has the pattern, 1, 3, 5.. You have one hand, 5 fingers, 3 spaces separating the fingers by knuckles etc... . Even the iris of your eye isn't a circle but something similar to spirals with a center hole. So in my opinion, Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: The Mathematical-Physics Solution For Short People... (Smart1234) The Mathematical-Physics Solution For Short People... I have noticed that society rejects short people. Why? Maybe they think tall people are better. Statistical analysis shows tall people get the best higher paid jobs, and the women are more attracted to them, and society even makes fun of short people with songs like Short People Have Nothing To Live For, etc.... . So for those that are short now, try not to feel too bad and rejected even though society doesn't accept you that much and makes you feel like a misfit reject. Some short people are made to feel like they are about 1inch tall, walked on, made to look like a funny fool idiot, and even made to have schizophrenia in extreme cases of rejection. But, with the Smart Model at least there is hope for them, if not in this world, maybe the next one. BECAUSE, The Smart Model has assisted in the revision the NEW Law of The Conservation of Matter and Energy. Which basically states that Matter and Energy can be Created, with mass and gravitational fields remaining relatively constant. So what does this mean? The only way to keep mass constant with mass being constantly created in the universe, is for people to grow with the increasing size with the universe. So I guesstimate that if you were 5'2 tall 10 years ago, you might be now about 5'4+ now, and you didn't know it, because the universe grows together with people. Eventually people ( within eternal time ) will be the size of a universe. So if you are short and ugly, try not to focus on that too much because YOU ARE STILL RELATIVELY GROWING in height and size and beauty. Who knows, the short person you think is short now, may actually be 6+ foot tall relative to the changes made in the growth of the universe. Now relative to the increasing size of the universe tall __10'____ O ^ / | | 10 years ago / | | short ___ | | O ^ / | / | | / | / __v__ / __ v_____ ( puny, little..) (looked down on..) Who knows short people may be 10' tall right now and didn't even know it and they ( society) are still calling them short and imperfect. (Spiritual View) I personally don't like the norms of society. I think people should be accepted the way they are and not what they look like or how much money they have. Sure I think we should all prosper and be beautiful ( inside and out), but at least we should have mercy on the short, disabled and poor people for now. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: The Mathematical-Physics Solution For Short People... (Smart1234) > tall __10'____ > O ^ > / | | > 10 years ago / | | > short ___ | | > O ^ / | > / | | / | > / __v__ / __ v_____ > ( puny, little..) > (looked down on..) how the Universe, and everyone in it, is expanding! Herc === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> In physics = as in A=B, means A is directly proportional to B >> multiplied by something very close to 1 most of the time. In computer >> engineering it means, A is now B, until I tell you otherwise. >Computer science might also describe '=' as A is copied from B. American hacker programmer languages like FORTRAN c c++ do that. Computer science languages like ALGOL's ADA's and PASCAL's use ':=' (becomes). Groetjes Albert P.s. there is now such thing as identity, there is just equivalence classes. (The notion that something is identical to itself is about as worthless as a truth can be.) -- -- Albert van der Horst,Oranjestr 8,3511 RA UTRECHT,THE NETHERLANDS One man-hour to invent, One man-week to implement, One lawyer-year to patent. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics <1Umvd.231528$HA.34538@attbi_s01> Discussion, linux) > P.s. there is now such thing as identity, there is just equivalence > classes. > (The notion that something is identical to itself is about as > worthless as a truth can be.) Utter nonsense. You do Dutch Computer Science no favors when saying something so stupid. -- At the Microsoft-sponsored cocktail reception in the Galaxy Ballroom that evening, Robert Dees urges us 'to network on behalf of the people of Iraq,' -- Naomi Klein reports on Microsoft's efforts to further democracy. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >In physics = as in A=B, means A is directly proportional to B >multiplied by something very close to 1 most of the time. In computer >engineering it means, A is now B, until I tell you otherwise. >>Computer science might also describe '=' as A is copied from B. > American hacker programmer languages like FORTRAN c c++ do that. > Computer science languages like ALGOL's ADA's and PASCAL's > use ':=' (becomes). Actually, '=' and ':=' often have the exact same semantic meaning: the imperative, 'Assign to A the value of B'; sometimes this is done by creating a copy and sometimes it is done by pointing A to B, in which case A and B are identical, and not just of equal value. The relationship to the mathematical symbol '=' (A is equal to B) is simply a convenient leveraging of the mathematical meaning into a different context with a modified meaning. In all computer languages the meaning of any symbol is defined in the interpretation: compiler, translator, virtual machine. > Groetjes Albert > P.s. there is now such thing as identity, there is just equivalence > classes. > (The notion that something is identical to itself is about as > worthless as a truth can be.) Not in programming, e.g. one item in a set might be iterating over all items in that set, in which case is very useful to be able to identify its self. -- Don't you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: The Smart DNA Model Reference( further topics online book The Smart Model) The Smart DNA Model It appears that there is more to the DNA than just chemical structures. According to the Smart Model, the spirial field that passes through the DNA has logical information in it analogous to a computer CD. If you notice the CD has a spiral of information stored in the spiral lines stored as on/off logic bit information which can be used as information transfer to your computer for further use. Where would this type information be stored in the Smart DNA Model? According to the Smart DNA Model there are different level of on/off sub-atomic bit states that influence the matter and energy interactions in the human body. Depending on the state of the DNA, chemical reactions occur as needed to assist the human body as needed. like for example, if you cut yourself, certain stored information in the DNA will know how to repair certain areas in the body such as the liver, stomach, brain, etc.., as needed. Stem Cells are like blank CD disks waiting to be filled with the needed information for atomic and sub-atomic level energy to matter and matter to energy interactions with the atoms and chemical structures themselves. But according to the Smart DNA Model, there is more logical information stored in it's Double Helix Spiral Field. Where is this additional information stored? As this field passes through the DNA, this information is pssed to the DNA in the cells. We are similar to living atomic ( and sub-atomic) biological ( ) (((()))) ( ) ------- ( ) (((()))) ( ) -------- ( ) (((())))) ( ) --------- ... and so on which forms the DNA. There is no uncertainty or electron randomness in an electron orbital field. The electron are precisely placed and used as current flow in the human body, which forms complex atomic level electric circuits which interact with the brain which is like a battery and neural logic process area. CW spinning information chains ( or strings) ( ) ( ) (((((( ))))))) ( ) ( ) CCW spinning information chains ( or strings) motion preserving the information as it goes from the outer external field to the inner internal field. The information loops endlessly. When the information occurs. Recent research has shown us that a nevre cell can program a silicon wafer chip and vise versa. The information is interchangable and can be programmed. Current research has experimented with implants that can influence the information in a persons brain. I am for the good aspects of this, but it could be dangerous if used for bad purposes. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: The Smart DNA Model >Reference( further topics online book The Smart Model) >The Smart DNA Model > It appears that there is more to the DNA than just chemical structures. >According to the Smart Model, the spirial field that passes through the DNA >has >logical information in it analogous to a computer CD. If you notice the CD >has >a spiral of information stored in the spiral lines stored as on/off logic bit >information which can be used as information transfer to your computer for >further use. Where would this type information be stored in the Smart DNA >Model? According to the Smart DNA Model there are different level of on/off >sub-atomic bit states that influence the matter and energy interactions in >the >human body. Depending on the state of the DNA, chemical reactions occur as >needed to assist the human body as needed. like for example, if you cut >yourself, certain stored information in the DNA will know how to repair >certain >areas in the body such as the liver, stomach, brain, etc.., as needed. Stem >Cells are like blank CD disks waiting to be filled with the needed >information >for atomic and sub-atomic level energy to matter and matter to energy >interactions with the atoms and chemical structures themselves. But according >to the Smart DNA Model, there is more logical information stored in it's >Double Helix Spiral Field. Where is this additional information stored? >CD. >As this field passes through the DNA, this information is pssed to the DNA in >the cells. We are similar to living atomic ( and sub-atomic) biological > ( ) > (((()))) > ( ) > ------- > ( ) > (((()))) > ( ) > -------- > ( ) > (((())))) > ( ) > --------- > ... and so on >the >structures, >which forms the DNA. There is no uncertainty or electron randomness in an >electron orbital field. The electron are precisely placed and used as current >flow in the human body, which forms complex atomic level electric circuits >which interact with the brain which is like a battery and neural logic >process >area. > CW spinning >information chains ( or strings) > ( ) > ( ) > (((((( ))))))) > ( ) > ( ) > CCW spinning >information chains ( or strings) >motion preserving the information as it goes from the outer external field to >the inner internal field. The information loops endlessly. When the >information >transfer >occurs. > Recent research has shown us that a nevre cell can program a silicon wafer >chip and vise versa. The information is interchangable and can be programmed. >Current research has experimented with implants that can influence the >information in a persons brain. I am for the good aspects of this, but it >could >be dangerous if used for bad purposes. Continued... used for? This allows for the erasing of unwanted information for a better improved logical information state to exist in the Smart DNA Model. So let's logic ( analogous spiral CD data), the brain can analyze this and erase the information as needed. When you rest at night, the brain fixes poor or bad information to make you feel refreshed the next day. Some information is too hard to erase which leads to mental illness, which can lead to physical sicknesses too. (Spiritual View) The better you understand how your body works maybe you and society will reach an enlightenment stage and learn to love one another and live in peace, and share in prosperity. It's hard to survive in a world of Dog eat dog. I have problems too and even with this knowledge, the negative field state hurts me. But with a better enlightenment of the world, we can change this field to one of positive states which lead us to better places in life. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Hydrogen Fusion Breakthrough Announcement >Hydrogen Fusion Breakthrough Announcement >25.12.04 16:00 EST >Review submitted by Hagelstein et al, the Correas - at the Aurora >Biophysics Research Institute Laboratories - have decided to make >public their breakthrough solution to the vexing problem of the >so-called Cold Fusion/LENR phenomenon. In a communication (The >Correa Solution to the Cold Fusion Enigma) that severely criticizes >both the DoE panelists and the five presenters of the submitted review >for having done such a poor job in their re-examination of the matter, >the Correas argue that the erratic results that continue to bedevil >the field stem from the actual lack of understanding of nuclear >processes that plagues modern physics and, in particular, the specific >slant of the five presenters of the submitted review. The Correa >announcement of an unsuspected solution to the so-called Cold >Fusion/Low-Energy Nuclear Reactions problem is bound to take Cold >Fusion researchers and their sponsors by surprise, especially now that >the DoE has confirmed and restated its negative 1989 opinion, and the >journal Science has put the subject back on ice. >As the Correas state in their communication, if Cold Fusion >researchers knew how to safely initiate and promote the desired fusion >pathway under room temperature conditions, and how to extract heat >from the electrodynamic interactions of protons, they would have long >ago done so and have collectively solved the problem of finding a >reliable, clean alternative energy source - free of any radioactive >emissions. Indifferent or even disdainful of the critical analytical >and experimental framework required to make sense of the complexity of >the observed interactions, they were unable to extract the pathway >outlined by the Correas - a pathway which produces neither neutrons >nor gamma radiation. The Correas comment on their design for the >Fusion Reactor employing the principles they have proposed: Energy, >they say, could be taken out as heat, or directly as electricity. >The Correa Solution to the Cold Fusion Enigma is available at: >http://www.aetherometry.com/correa_nuclear_fusion.html I seems like I told people this 10 years ago with the Smart Fusion Model. You mean they're finally realizing this? Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: Hydrogen Fusion Breakthrough Announcement > I seems like I told people this 10 years ago with the Smart Fusion Model. You > mean they're finally realizing this? It is bullshit. I have yet to see one net kilowatt produced by controlled fusion. Fuion has been 30 years in the future for the last 50 years. Bob Kolker === Subject: Re: Hydrogen Fusion Breakthrough Announcement >> I seems like I told people this 10 years ago with the Smart Fusion Model. >You >> mean they're finally realizing this? >It is bullshit. I have yet to see one net kilowatt produced by >controlled fusion. >Fuion has been 30 years in the future for the last 50 years. >Bob Kolker I which I could show you, The Smart Fusion Model ( theoretically). I couldn't post it. I felt that the world wasn't ready yet for this information. The Smart Fusion Model theoretically shows that it could produce the same results of the amount of energy as an atomic bomb, with energy regulation, (((if))) the methods shown in The Smart Fusion Model is used. In fact, it's so dangerous, in my opinion, I think an average person ( with about $200,000.00) could use things on the market right now and build one, if he knew how. Senator to pass new legislation, in case they figure out how to do it. Because even though fusion has good uses, the bad side of the use, is the problem. It may even be possible to build a Fusion Bomb. In fact, a Hydrogen Bomb IS a fusion bomb. But the techniques used to make the Hydrogen Bomb was a lucky chance. The Smart Fusion Model uses no chance or luck. It is precise. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Help with def of ordered pair I'm need help proving that if (x,y) denotes a set {{x},{x,y}} then (x,y)=(u,v) for any x, y, u, v, iff x=u and y=v. The text says that after successfully prooving this I can treat it (x,y)={{x},{x,y}} as the definition for an ordered pair. They give a hint to consider two cases: when x equals y and when x is not equal to y noting that {x,x}={x}. Can someone help me get started. Perion === Subject: Re: Help with def of ordered pair > I'm need help proving that if (x,y) denotes a set {{x},{x,y}} then (x,y)=(u,v) > for any x, y, u, v, iff x=u and y=v. The text says that after successfully > prooving this I can treat it (x,y)={{x},{x,y}} as the definition for an ordered > pair. This is from Spivak's Calculus, right? > They give a hint to consider two cases: when x equals y and when x is not equal > to y noting that {x,x}={x}. Can someone help me get started. You have to prove two assertions: 1) if (x,y) = (u,v), then x = u and y = v; 2) if x = u and y = v, then (x,y) = (u,v). I think that the second one is trivial. Do you agree? Concerning the first one: if (x,y) = (u,v), that is, if {{x},{x,y}} = = {{u},{u,v}}, then both sets must have the same number of elements, which is either 1 or 2. If it is 1, then y = x and {{x},{x,y}} = = {{x},{x}} = {{x}} and, for the same reason, {{u},{u,v}} = {u}. If both sets have 2 elements, then... I hope that this helps. Jose Carlos Santos === Subject: Re: Help with def of ordered pair >> I'm need help proving that if (x,y) denotes a set {{x},{x,y}} then >> (x,y)=(u,v) for any x, y, u, v, iff x=u and y=v. The text says that after >> successfully prooving this I can treat it (x,y)={{x},{x,y}} as the definition >> for an ordered pair. > This is from Spivak's Calculus, right? It's from The Zakon Series on Mathematical Analysis - Basic Concepts of Mathematics (Vol 1) >> They give a hint to consider two cases: when x equals y and when x is not >> equal to y noting that {x,x}={x}. Can someone help me get started. > You have to prove two assertions: > 1) if (x,y) = (u,v), then x = u and y = v; > 2) if x = u and y = v, then (x,y) = (u,v). > I think that the second one is trivial. Do you agree? Yes - no problem with that one. Simple substitution of equals. > Concerning the first one: if (x,y) = (u,v), that is, if {{x},{x,y}} = > = {{u},{u,v}}, then both sets must have the same number of elements, > which is either 1 or 2. If it is 1, then y = x and {{x},{x,y}} = > = {{x},{x}} = {{x}} and, for the same reason, {{u},{u,v}} = {u}. If > both sets have 2 elements, then... > I hope that this helps. > Jose Carlos Santos Perion === Subject: Linear functional by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiTw19332; I need help in showing that: If V is vector space,(x_n) is sequence of linearly independent vectors and (a_n) is sequence of scalars,then there is linear functional F defined on the span of (x_n) such that F(x_n)=a_n. === Subject: Re: Linear functional at 04:44 PM, anonymous@mathforum.org (Fabian) said: >If V is vector space,(x_n) is sequence of linearly >independent vectors and (a_n) is sequence of scalars,then there is >linear functional F defined on the span of (x_n) such that >F(x_n)=a_n. Consider the definition of linearly independent vectors and of span. If x is in the span, then x can be exspressed as x = Sigma b_n*x_n in one and only one way. >Can you please solve this? Prove and apply the above. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail 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 === Subject: Re: Linear functional >I need help in showing that: >If V is vector space,(x_n) is sequence of linearly >independent vectors and (a_n) is sequence of scalars,then >there is linear functional F defined on the span of (x_n) >such that F(x_n)=a_n. Hint: every vector in the linear span of (x_n) is uniquely expressible as a (finite) linear combination of these vectors. So what should F(sum_n c_n x_n) be? Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Linear functional Are you talking about x_n for n=1,2,3,... ;in an infinite dimansional vector space ,In this case you need Zorn's lemma to extend to a basis for V.In any case there is a set S of vectors containing all the x_n , such that every vector in V is uniquely a finite linear combination of vectors from S. If v is in V v = Sum( b_nx_n ) + Sum (finite linear combinations of vectors in S^1) where S^1 is S with the vectors of the sequence x_n removed .Note in the first sum that b_n =0 for all but finitely many n so it is also a finite sum and makes sense (drop out the zero terms). F(v)= Sum(b_n x_n) (also efectively a finite sum) gives the === Subject: Re: Linear functional Sorry,If you just want F only on Span((x^n) =finite linear combinations of vectors x_n then F(v) =Sum (b_na_n) for v =Sum(b_nx_n) (effectively finite sums) In the more general case considered above th penultimate line has a misprint,x_n should be a_n in the definition of F so again F(v) = Sum(b_na_n) where all but finitely many b_n's are zero.Stuart M === Subject: Re: Linear functional >Are you talking about x_n for n=1,2,3,... ;in an infinite dimansional >vector space ,In this case you need Zorn's lemma to extend to a basis >for V. He's not asking about a linear functional on the whole vector space. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: !!!! f^ [2 005 ] ( x ) = x . ? ? ? ? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiTQ19323; Tell all and everything you fancy , think , believe , about it. A V (E) === Subject: Re: brainteaser by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiVm19394; >> an ant, traveling at uniform speed, takes one minute to crawl from one end of >> a >> ruler to the other and fall off. when two ants run into each other, the rule >> is >> that each turns around and goes the other way. if we throw 5 ants at random >> onto the ruler (they all hit the ruler at the same time, and then choose a >> direction to crawl at random, every one of them always traveling at the same >> uniform speed -- 1 ruler length per minute), what is the least amount of time >> needed to guarantee that all 5 ants have fallen off the ruler? >> I believe the answer is 1 min ... but can someone show me how this can be >> proven? >Proving it only requires that some combination of positions and >directions be found which takes one minute to clear all the ants, and >such an arrangement is trivially simple to construct. Huh? How does the existence of such a combination preclude the existence of a combination that takes more than a minute to clear? === Subject: Re: The state-of-the-art in mathematics by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiUk19340; >> Extending a mathematical space, including the adjoining of any >> mathematical object, does not well-define that larger space. >The grinding sound we hear is that of a Crank turning. >Bob Kolker Since I can.89t find any trace of mathematics in your posts I tried to search the databases for any clues about your credibility. You know what? My PC crashed! I then looked for your name in the list of mathematicians under the Mathematical Genealogy Project. It hanged up again! Are you, perhaps, an undergrad math major? Can.89t be since you don.89t even know what a real number is. Tell me: where did you get your training in mathematics, if any? The only conclusion I have is that you are a charlatan. I think I wasted my time on your nonsense. E. E. Escultura University of the Philippines === Subject: Re: The state-of-the-art in mathematics > Since I canÍt find any trace of mathematics in your posts I tried to > search the databases for any clues about your credibility. You know > what? My PC crashed! I then looked for your name in the list of > mathematicians under the Mathematical Genealogy Project. It hanged up > again! Are you, perhaps, an undergrad math major? CanÍt be since you > donÍt even know what a real number is. Tell me: where did you get > your training in mathematics, if any? The only conclusion I have is > that you are a charlatan. I think I wasted my time on your nonsense. I am 69 years old and I have forgotten more mathematics than you ever knew in the first place. Bob Kolker === Subject: Re: Counterexamples to FLT by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiUp19357; >the integers are isomprphic to crediting & debiting stuff; >is that the sense of Diophantus? >please, extend your Dark Field to the complex plain! > The dark number d* = N - (N-1).99... = 1 - 0.99..., >> I forgot to mention in this message that the integers has not valid >axiomatization. So, FLT is still ill-posed even in the integers. I >fixed this problem by embedding the integers in the new real number >system. >--ils ducs d'Enron! The complex plane is not well-defined because i is supposedly the solution of the equation x^2 + 1 = 0 among the real numbers which does not exist. A concept is well-defined if its existence, properties and relations with other concepts are specified by a consistent set of axioms. E. E. Escultura >http://tarpley.net/bush22.htm === Subject: Re: Counterexamples to FLT >the integers are isomprphic to crediting & debiting stuff; >is that the sense of Diophantus? >please, extend your Dark Field to the complex plain! > The dark number d* = N - (N-1).99... = 1 - 0.99..., >> I forgot to mention in this message that the integers has not valid >axiomatization. So, FLT is still ill-posed even in the integers. I >fixed this problem by embedding the integers in the new real number >system. >--ils ducs d'Enron! > The complex plane is not well-defined because i is supposedly the solution of > the equation x^2 + 1 = 0 among the real numbers which does not exist. A > concept is well-defined if its existence, properties and relations with other > concepts are specified by a consistent set of axioms. I looked at your website. You claim to have a Ph.D. in mathematics. I am wondering how you could manage to do that, yet be unaware of any of the the standard constructions of the complex numbers. === Subject: Re: Counterexamples to FLT > The complex plane is not well-defined because i is supposedly the > solution of the equation x^2 + 1 = 0 among the real numbers which > does not exist. A concept is well-defined if its existence, > properties and relations with other concepts are specified by a > consistent set of axioms. And they are. The complex number field can be represented as a subgroup of GL(2). The complex number a + b*i is represented by the matrix |a -b| |b a|. The groups of such matrices under + and * exactly reproduce the complex numbers. Has anyone ever told you that you are a complete mathematical incompetent. No? O.K. Then I will. You are a complete mathematical incompetent. Bob Kolker === Subject: Re: Counterexamples to FLT > The complex plane is not well-defined because i is supposedly the > solution of the equation x^2 + 1 = 0 among the real numbers which > does not exist. A concept is well-defined if its existence, > properties and relations with other concepts are specified by a > consistent set of axioms. > And they are. The complex number field can be represented as a subgroup > of GL(2). The complex number a + b*i is represented by the matrix > |a -b| > |b a|. > The groups of such matrices under + and * exactly reproduce the complex > numbers. > Has anyone ever told you that you are a complete mathematical > incompetent. No? > O.K. Then I will. You are a complete mathematical incompetent. > Bob Kolker Seconded! === Subject: Re: The state-of-the-art in mathematics by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiVR19434; >> Extending a mathematical space, including the adjoining of any >> mathematical object, does not well-define that larger space. >The grinding sound we hear is that of a Crank turning. >Bob Kolker Since I have not found any trace of mathematics in your posts I'll make a simple test that can unmask your ignorance: well-define a real number. Now put your money where you mouth is. If you can give me a correct answer I'll send you a check for $1000; if you can't I'll just put you in my list of charlatans and mathematicians from antiquity. E. E. Escultura University of the Philippines === Subject: Second time request by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBQGiWj19456; This is the second time to announce this. Critiques to the following paper http://jp.arxiv.org/PS_cache/math/pdf/0407/0407470.pdf would be really appreciated. By the way, a little news on the paper. If we put a rectangle with two triangles (i.e., like a pencil with both ends sharpened) instead of a rectangle, the method obviously does not work; to see this, just try to draw one with the new shape. You will have a point inside a curve through which lines pass more than once. This makes me think that the original method may also suffer from a point which we can not see in simple drawing. A happy new year to all the professors and students who are making this newsgroup very enjoyable, H. Shinya === Subject: Re: Second time request > Critiques to the following paper > http://jp.arxiv.org/PS_cache/math/pdf/0407/0407470.pdf > would be really appreciated. A comment on the preprint On a method for obtaining a planar region with two equichordal point is here: http://www.math.ohio-state.edu/~edgar/equichord/ The method does _not_ produce a continuous curve. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Second time request Your comment is very dry G.A.. - and at the same time You put so much work in it. Isn't the result beautiful, or at least nice ? Math and emotions are not contradictionary. Anyhow, i want to thank You for Your work. the question was intriguing me too and actually i was near the point, thinking, that it can't be done. Okay, the proof is disproofed - but this can be still a starting point for further math and You did an important contribution. I hope Hisanobu will be satisfied too, but still hungry for more investigation. Happy 2005 Hero === Subject: Re: Second time request The link starts: On a Method for Obtaining a Planar Region with Two Equichordal Points Hisanobu Shinya Abstract A point on a planar region is said to be equichordal if all chords through the point have the same length. We briefly present a method with which we can show the existence of a planar region with two equichordal points I didn't study it yet. Of course circles is the first one thinks of, but a region with one equichordal point doesn't have to look like a circle. I tried to visualize the problem with these dynamical geometry programms (it could be done by mechanical means also): You fix two points to the paper or on your monitor. You define a moveable line through each point. Where these lines intersect, You connect the lines- that is, you define a moveable point, which is on both lines. When you grab this point with the mouse and move it around, the two lines will have to follow and to rotate in their fixpoints on the background. Now measure on both lines an equal length from this common point. The two endpoints will have to leave a trace, and the grabbing point too. Can You do a full turn around the two fixpoints getting back to the start and - that's the problem - so, that all three points are moving on one trace, on a line, more or less bend. Did i get it ? I hope experimenting with this, will give You pleasure, and if - if! - You succeed, please show us Your drawings. Hero === Subject: Re: Polysigned Numbers The multiplication of Tim's polysigned numbers is new (as far as i know) and an investigation might turn out more rewarding than the study of let's say pseudo-irrelevant numbers. And it's relaxing from the stress of overspecialized activity. Although algebraically different, a representation is given by the ordinary vector-arrows of ray, line, plane and space (algebraically denoted here as one-signed (one sign written with one stroke : - ) , two-signed ( adding a sign with two strokes : + ), three-signed ( -,+,*) and four-signed (-,+,*,# ). Through Tim's definition of multiplication the postive reals are embedded in all four, with the highest sign (in three-signed with *, in four-signed with #), so equal signs are not denoting equal directions in three-signed versus four-signed. And also the angle between two rays differ in different dimension : in two-signed 180 degrees, in three-signed 120 degrees and in four signed about 109 degrees. Traveling to a foreign country one always looks for familiar things as starting-point, to compare to and to see differences and similarities. How is a vectorarrow with opposite direction given in three-signed and four-signed? Now, algebraically signs are corresponding to components of a tupel, so in four-signed * is the m-component of (k, l, m ,n). Geometrically they are represented by direction, in three-signed - is north-west, + is south-west and * is east. (compare this to the four-directions of a plane: in common notation: + for east(positive x-axis), + sqrt of - for north(positive y-axis), - for west (negative x-axis) and - sqrt of - for south (negative y-axis).) Remembering the basic sum-rule for polysigned - a&+a=0 in two-signed -a&+a&*a=0 in three-signed -a&+a&*a&#a=0 in four-signed (where & is the sum-symbol) one finds the opposite to -2&+3&*2.76.9 after reducing (like 6 /8 reduces to 3 /4) - 0&+1&*0.76.9 as - 5.9&+4.9&*5.14�, cause both add up to Zero. Now to multiplication in 3D, that is in three dimension of space, here corresponding to four mathematical dimensions of polysigned numbers: it's different from Quaternion- multiplication ( and multiplication with a scalar and dot-multiplication and cross-multiplication). One striking obeservation: the multiplication of any vector with #b or (0,0,0,b) does not change direction and changes value (length) by factor b. So a vectorarrow may be written as a linear- combination of a #-part-arrow and the rest. But this is only true in three of the four compartments of space. So look into the compartment opposite the #-direction at the -b&+b&*b or (b,b,b,0) vector.This one - by multiplication - just mirrors or rotates by 180 degrees any vectorarrow to the opposite and scales it by the factor b. So every arrow in this compartment can be calculated from an arrow -b&+b&*b or (b,b,b,0) plus a rest. And the rest-arrow has in reduced form in all of the four compartments only maximal two components not zero. This needs verifiaction and for this it would be nice, if we know, what algebraic rules are valid here, like commutativity or distributivity and else. And finally for now, it leaves the investigation how to visualize the multiplication of these rest-arrows. Enjoy. Hero PS.There is an interesting point in this polysigned for friends of the art of vectorcalculation on the plane, like people working in a branch of log z or travellers on Riemann's surface. Tim is not actually embedding the positve reals with the #-axis (ray) -let me show You with complex numbers. If one wants to express the point on a plane not in cartesian, but in polar coordinates, he expresses direction by an orientated angle, which gives the difference of direction to a reference direction, most often the direction of the positive x-axis. And this angle is between 0 and 2*pi or 360 degrees. But to be exact, one chooses |0,360), the point zero is included, so 360 is excluded, others choose |-180,180) or (-180,180| .Always the positve scalars are included. Doing similar to Tim with polysigned, one has to take (0,360| , the reals not embedded, staying outside in the scalar-domain. Or consider a different modulo definition, like a number modulo 5 is 1, 2, 3, 4 or five in place of 0,1,2,3,4. === Subject: Re: Polysigned Numbers > The multiplication of Tim's polysigned numbers > is new (as far as i know) and an investigation might turn > out more rewarding than the study of let's say > pseudo-irrelevant numbers. may understand better than my own. I have been trying to get a formulaic reciprocal out of four-signed ( S(4)) numbers. So that: z1 z2 = # 1 . Then z2 is the reciprocal of z1 and vice-versa. But there is not always an answer. This sent me back to finding quotients which nets another twisted result: the answers of a known product when reversed to a quotient provides a parametric solution. So for example: (- 1 + 1)(- a + b * c # d) = + 1 * 2 # 1 . This has a known solution of (- 1 + 1) . So now I know that this particular equation does have a solution. Working through the algebra yields: ( 3, x - 1, 2, x - 2 ) where these are in (-,+,*,#) form and the contents (a,b,c,d) are real valued. The following are solutions to this parametric equation: - 3 + 2 * 2 # 1 , - 3 + 4 * 2 # 3 , - 3 + 20 * 2 # 19 . So, on top of the nonorthogonality of the number system there is a nonorthogonal quotient solution for some problems. The general n-signed product has symmetry. But the meaningfulness of that product is questionable. All of the associative and commutative laws for product and sum will work for n-signs (though I do not have a formal proof of this a few computations will readily demonstrate this). Traditional mathematical concepts in this domain are not necessarily applicable. I wish someone with a strong philosophy on the various products and their value could comment. http://BandTechnology.com/PolySigned/PolySigned.html -Tim === Subject: Re: Polysigned Numbers Your questions are good: I have been trying to get a formulaic reciprocal out of four-signed (S(4)) numbers. So that: z1 z2 = # 1 . Then z2 is the reciprocal of z1 and vice-versa. the answers of a known product when reversed to a quotient provides a ........ solution. So for example: (- 1 + 1)(- a + b * c # d) = + 1 * 2 # 1 . Your answers are wrong. How to compute the product? Consider a register with four places: (-,+,*,#) in each place You have a real number >=0. If You multiply by -a every value is scaled by a and every value has to move to the right through the register, and the one falling off must move to the empty first place. If You multiply by *a they have to repeat this process two times. In machine-code there's a command doing just this with a byte of zeros and ones. Now when one multiplies two foursigned, one will get the sum of four such foursigned numbers. You write: on top of the nonorthogonality of the number system there is a nonorthogonal quotient solution for some problems. The general n-signed product has symmetry. This has meaning for me only if i know Your definitions of:: the nonorthogonality of the number system nonorthogonal quotient product symmetry You write: I wish someone with a strong philosophy on the various products and their value could comment. And i wish for You, that You would find out all the nice results by Yourself, have fun doing this. And when You post them here, that You can get conformation of Your results. Have fun Hero === Subject: Re: Polysigned Numbers I certainly stand by the quotient presentation. (- 1 + 1)(- 3 + 20 * 2 # 19) = + 1 * 2 # 1 And (- 1 + 1)(- 3 + 2 * 2 # 1) = + 1 * 2 # 1 And (- 1 + 1)(- 1 + 1) = + 1 * 2 # 1 . What do you call a system that has two or more representations for the same value? I thought that the correct term is nonorthogonal. To apply the term to a solution of a problem may be stretching the strict definition. I am not sure. This does show the glaring magnitude problem in four-signed math. My random number attempt to find the extremes of the magnitude error on my website is clearly not covering this result. This would show a min of 0 for the worst case magnitude comparison. The random number attempt got down to only 0.01 . http://www.bandtechnology.com/PolySigned/PolySigned.html I do not understand what it is that you disagree with in the quotient analysis. - Tim === Subject: Re: Polysigned Numbers Yes , You calculated right. I did it wrong and i want to apologize. Sorry. So it's really unique: A polysigned numbers has not one but a couple of multiplicative inverse (a times b=1 yields several b for a given a) That's really an important step and i hope for more to come Hero === Subject: Re: Polysigned Numbers One of us had to have something backwards. I'm just glad it was you and not me. But one of these days it will be me. Now, the chosen quotient analysis happened to have a square solution: ( - 1 + 1 )( - 1 + 1 ) I have yet to find one that is not a square solution. I have not tried very hard yet but it would be very interesting if it was unique to squares. I think that I am ready to go toward a vector representation. But how to index on the computer in text is not familiar to me. Are there standards? Is there an easy way to represent the multiplication in vector format that is general? One of the things that makes me want to push for this is the ability to do vector additions and subtractions so that a vector p1 and vector p2 have a difference vector p1 - p2 . But this sign is completely different from the minus sign of polysigned numbers. In polysigned the representation of a negative of a number in three-signed is: Neg( - a + b * c ) = ( + a * a - b * b - c + c ) . This is not generally represented by the minus sign, though it happens to for two-signed numbers. Vector math does work with the geometrical representation of polysigned numbers so it would be nice to not have to go to new representations. I do not believe that this is a notational mistake on my part. It is more that the reals have a confluence with vector superposition that made for an obvious redundant choice of symbolism. Anyhow, by going to vector form the elementary signs will be indexed and the old intuitive minus and plus signs can be used for summation and negation. I think probably the only person that would be confused by that is me. Many people have asked for this. I would like to put the identity sign at index zero. This will preserve its position and would coincide with the @ symbol being a zero sign (equivalent to the upper identity sign) which has been discussed for the elementary approach. Help please. -Tim === Subject: Re: Polysigned Numbers Just stay with Your notation and translate to tupel like this (in four-signed): -a =(a,0,0,0) *c=(0,0,c,0) and so forth. Addition or sum is done, as with all tupels by component addition: (a,0,0,0) plus (0,0,c,0)=(a,0,c,0) or (a,0,0,0)plus (a,0,0,0)=(a plus a, 0,0,0). Your speciality is of course (b,b,b,b)=(0,0,0,0) Now for negatives , with vectors one looks for vectors into the opposite direction. To calculate these, just remember that a vector and the opposite vector adds up to zero, f.e.: -2.1+3*0#5=(2.1,3,0,5) just take any real equal to or bigger than these four components, so >=5 and (5,5,5,5)=(0,0,0,0) Now 2.1 plus 2.9=5, 3 plus 2=5, 0 plus 5=5 and 5 plus 0=5, so the opposite vector is (2.9,2,5,0). Of course Your way of building (0,2.1,2.1,2.1)plus(3,0,3,3)plus ((0,0,0,0)plus(5,5,5,0) = (8,7.1,10.1,5.1) gives the same result. So, if You want to find the difference of two vectors p1 and p2, you calculate the vector opposite of p2 and add it to p1. To multiplication f.e (2,7,1,1) times (4,5,9,3) first component times first component gives 2 times 4 into the (one plus one=)second component, plus...., second component times third component gives 7 times 9 into the (two plus three=) fifth component. And the fifth is in four signed (five - four)=one, the first component,plus... and so forth. The number of strokes of Your signs correspond to the index-number, or the number of the component. Is this, what You are asking for ? Have fun Hero PS. A nice result one gets, if one multiplies these two numbers (both unequal to zero): (-1+1) times (-1*1) or in components (1,1,0,0) times (1,0,1,0). === Subject: how to prove Apparently the product of any two reflections (in solid space) is a rigid motion. How does one prove this? Peace, STM === Subject: Re: how to prove > Apparently the product of any two reflections (in solid space) is a > rigid motion. How does one prove this? Clifford Algebra is an especially useful tool for dealing with reflections and rotations (too bad Pertti's not around) In the Clifford Algebra, a reflection of vector v about a unit vector u is uvu. The product of two reflections u and w is wuvuw, and that is clearly a rotation in the plane containing both u and w. === Subject: Re: how to prove Working in R^3 with the usual inner product , A reflection is a composition of of one that fixes 0 and a translation so we can reduce to the case where both reflectiions fix 0. Then a reflection is a linear transformation T which fixes all the points of some 2 dimensional subspace W and which takes a unit vector N orthogonal to this subspace to -N.Let A,B be unit vectors in W which are orthogonal so that A,B,N is an orthonormal basis for R^3. Then T takes A,B,N into A ,B,-N (also orthonormal) Hence T is an isometry of R ^3 and takes any orthonormal basis into another orthonormal basis.However det(T) =-1 .But if T^1 is another reflection then TT^1 also takes orthonormal basis to orthonormal basis,and is thus an isometry also.But det(TT^1) =det(T)det(T^1) =(-1)(-1)=1 and hence is a rotation which is a rigid motion (the last time I checked). So you need to know enough linear algebra to know a rotation can be === Subject: Re: how to prove |Apparently the product of any two reflections (in solid space) is a |rigid motion. How does one prove this? It's not true. It could also be a rotation. Keith Ramsay === Subject: Re: how to prove >|Apparently the product of any two reflections (in solid space) is a >|rigid motion. How does one prove this? >It's not true. It could also be a rotation. When is a rotation not a rigid motion? Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: how to prove |>|Apparently the product of any two reflections (in solid space) is a |>|rigid motion. How does one prove this? | |>It's not true. It could also be a rotation. | |When is a rotation not a rigid motion? Sorry, for some reason I was thinking a rigid motion was a translation! To know how to prove this, I think I would need to know which definitions of reflection and rigid motion are being used. Probably the original poster is aware that a reflection is an isometry and that a composition of isometries is an isometry. But to be a rigid motion, it needs to be orientation preserving. How has rigid motion been defined for the original poster? Keith Ramsay === Subject: Re: how to prove > needs to be orientation preserving. How has rigid motion > been defined for the original poster A rigid motion is one that preserves distances. Also known as an isometry. Some people exclude reflections from this class of motions. Bob Kolker === Subject: Re: how to prove |How has rigid motion been defined for the original poster? |A rigid motion is one that preserves distances. Also known as an |isometry. Some people exclude reflections from this class of motions. I'm pretty sure the original poster is working with a definition that excludes orientation-reversing isometries, or else proving that the composition of two reflections is one is a lot less interesting-- all it would take is to show that the reflections themselves are isometries and that isometries compose. Excluding ordinary reflections is not quite enough, since there are other orientation-reversing transformations such as glide reflections, e.g. (x,y,z)->(x+1, -y, z). If the definition includes only orientation-preserving isometries, then the issue is which definition of orientation preserving was used. After all, once the theory of orientation is thoroughly developed, then it's simply a matter of noting that the composition of two orientation-reversing transformations is orientation-preserving. Just how much is left to prove, there, depends on where in the development of the theory of orientation one is. I like the definition offered by another poster, that a rigid motion is an isometry path-connected to the identity. One approach that would make sense under some treatments is to continuously vary the second reflection until it coincides with the first one. This gives a continuous path from the composition of the two original reflections and the identity. Of course, I haven't defined continuity anywhere. Hope the original poster has gotten what he needed from the discussion. Keith Ramsay === Subject: Re: how to prove Yes,very nice.Perhaps the original poster would like to know that there is a proof that SO(n) (isometries fixing 0 ,with det=1,or equivalently orientation preserving isometries with 0 fixed) is connected (ie there is a path from any point to the identity) in the recent book by John Lee :Intro === Subject: Re: how to prove <_a%zd.713689$mD.5860@attbi_s02> Nobody should call it a rigid motion unless it is on a continuous 1 parameter group of isometries starting from the Identity,which is equivalent in the case where 0 is fixed to being a linear isometry with === Subject: Re: how to prove >>|Apparently the product of any two reflections (in solid space) is a >>|rigid motion. How does one prove this? >>It's not true. It could also be a rotation. >When is a rotation not a rigid motion? I was told we wouldn't have to read koans on this BBS. Lee Rudolph === Subject: Re: how to prove Make a drawing of a point, being reflected on one line, and the result being reflected on a different line. Try to abstract to definitions of reflections on a line, of product and of rigid motion. Then generalize. Show here Your results. have fun Hero