a naive question : given the uncertainties (confidence intervals) in CODATA, how good is the fit, or, what is the (combined) probability that the Plouffe-values are 'real', and the variances due to chance errors? Particle Ratio ; Value; Plouffe; NumericalPlouffe Neutron-Proton; 1,001378419; L[9] L[6]^(1/2) / Phi^12; 1,001378267 Alpha particle-Electron; 7294,299536; L[5] Phi^17/L[7]^(1/2); 7294,299151 Tau-Muon; 16,8183; Phi^9 L[10]^(1/11) /L[4]; 16,81830004 Helion-Proton; 2,993152667; Phi^13 L[3]^(1/18) /L[3]/L[8]; 2,993155303 Neutron-Electron; 1838,68366; Phi^19 L[4]^(17/19) /L[7]; 1838,685785 Rest mass of alpha particle-electron; 7349,672665; Phi^(61/2)/L[12]; 7349,658428 Proton-Electron; 1836,152673; L[4]^(11/30) L[8]^(53/30); 1836,152847 Muon-Electron; 206,7682838; F[5]^(1/15) L[4]^(7/15) L[5]^(9/5); 206,7682818 Neutron-Muon; 8,89248402; L[5] F[5]^(11/5)/Phi^(39/5); 8,89248417 Proton-Muon; 8,88024333; Phi^(37/30) F[5]^(7/15)L[5]^(7/20); 8,880243302 Helion-Electron; 5495,885269; L[9] Phi^13/L[5]^(14/17); 5495,856824 Alpha-particle-Proton; 3,972599689; Phi^18 L[11]^(8/15) /L[10]/L[11]; 3,972595175 Deuteron-Electron; 3670,482965; L[2]^3 Phi^(8/29) L[8]^(36/29); 3670,482964 Wouter. ----- Original Message ----- From: "Simon Plouffe" <simon.plouffe@sympatico.ca> To: "math-fun" <math-fun@mailman.xmission.com>; "Eric W. Weisstein" <eww@wolfram.com>; <sfinch9@hotmail.com>; <D.Broadhurst@open.ac.uk>; "Jean-Paul Allouche" <Jean-Paul.Allouche@lri.fr>; <delahaye@lifl.fr>; <davis@math.toronto.edu> Sent: Friday, March 12, 2004 9:59 PM Subject: [math-fun] a search for a mathematical expression using a large database
Hello everyboy,
I made an experiment over a period of several months using my inverter (the home version with 610 million constants).
I took the latest values of the CODATA 2002 NIST table of physical constants and tried a vast experiment to find any reasonable mathematical expression for those ratios. http://physics.nist.gov/cuu/Constants/Table/allascii.txt
That data is from december 2003.
I used many simple and naive models to try to find anything, any possible expression as long as it is simple, short and easily explained.
Here are the results : http://www.lacim.uqam.ca/~plouffe/Search.htm
Important note : that article (preprint) is an exercice in numerical analysis and an attempt to find a mathematical and simple expression and NOT any attempt to any physical theory. My knowledge of physics is naive and probably outdated. I have no idea if this is making any sense in the real physical world. It is only <the best possible mathematical expression> that could exist for those numbers that have been found using what I believe are appropriate tools.
The tables I used are the ones on the Inverter and a set of specialized tables constructed from the OEIS and my own tables that are not yet public.
There are 2 main findings : First I discovered a weakness in the PSLQ, LLL or integer relations algorithm that only exist for a specific type of numbers. Second, I propose a set of at least 12 values among the 28 known values (actually there are 14 + inverses). In other words, I have a mathematical expression for 12 of the 14 values. These expressions are all generated by 1 number only.
The second finding is related to the first as explained in the article.
The article (preprint) as been submitted to a known periodical.
Simon Plouffe
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