Essay Abstract
"SEPHIROT": EMET!!!: "Known Unknowns Versus Unknown Unknowns": It's a Jack-in-the-Box Universe: Ten-Digits; Log-Law Scale-Invariance; Utter-Simplicity: "Complexity" Versus "Complicatedness"; Zipf's-Law/ Hyperbolicity/ Inevitability (Archimedes); Bose- {Euler[(1732)] over-reals R)∑_(k=1)^∞▒〖1/k^R =∏_P▒1/((1-1/P^R ) )〗= ∏_P▒P^R/((P^R-1) ) ~ ∏_ω▒e^(ħ(ω-z)/kT)/((e^(ħ(ω-z)/kT)-1) ) }-{Riemann, "Ueber die Anzahl der Primzahlen unter einer gegebenen Groesse", Monatsberichte der Berlin Akademie,(1859)] over-complex-numbers C): ∑_(k=1)^∞▒〖1/k^( C) =∏_P▒1/((1-1/P^( C) ) )〗= ∏_P▒P^( CC)/((P^( C)-1) ) ~ ∏_ω▒e^(ħ(ω-z)/kT)/((e^(ħ(ω-z)/kT)-1) )}-{Bernoulli-Newcomb[Am. J. Math. 4, 39(1881)]-{Planck(1901)]}-{Einstein(1905)]-Poincare[(1912)]-Weyl[Goett. Nach.???(1914); Math. Ann. 77, 313(1916)]-Bose(1924)-Einstein(1925)]-VS. Fermi(1927)-Dirac(1927)-Benford[J. Am. Phil. Soc. 78, 115(1938)]-Kac["The Mathematics of Statistical-Reasoning" (1955)]-Raimi[Sci. Am.(1969) ]-Hill[Proc. Am. Math. Soc.123,3,887(1995)logarithm-function scale-invariance("MAGNIFICAT", (Bach) proof]-Jech(1995)-Siegel, Antonoff, Pi, Smith[Am. Math. Soc./Math. Assn. Am./SIAM Joint Mtg., San Diego(2002)] -Benson[last-lecture!!!: Workshop: "Cohomology and Support of Algebraic-Representation-Theory", Julia Petsova, Eric Friedlander and David Benson eds., Pacific Institute for Mathematical Studies, University of Washington(2012)]-Chern[????]-Hirezbruch, Riemann, Roch Theorem!!! Finding and proof of a digits on-average[CAUSING] logarithmic-law 〈P〉=〖log〗_10 (1+1/d), by mathematicians mistakenly excluding physics-crucial d = 0 singularity/pole, as log-law 〈P〉=〖log〗_10 (1+1/(d∈[1,...,9] )), but in actuality purposely including the all-important physics-crucial d = 0 singularity/pole: 〈P〉=〖log〗_10 (1+1/(d∈[0!; 1,...,9] )) permits "EMET"/TRUTH, purposely sans any "specificity-of-(so miscalled)"complexity" tactics: NO: models("standard" nor any other), mechanisms, processes, parameters(proliferation: ad infinitum; ad nauseum!!!), "Digits"' classic (but not classical!) Newcombe(1881)-Poincare(1912)-Weyl(1914; 1916)-Benford(1938) "NeWBe-Law" P(d) = log10 (+1+1/d) [integer d * [0,9]] * Z ; versus, non-integer 0 < P < 1] (on average) statistical-correlations, with recent Browne-Hill-Mathews-Greespan popularizations, based upon recent Hill-Jech-Pietroniero ostensibly-"rigorous" proofs domination by [(logarithm-base - invariance) = (units-invariance) = (SCALE-invariance)], and Nigrini-Hill-Burton widespread forensic applications to fraud-detection, with indictments, prosecutions and convictions, has gotten Wall Street's attention, after Peters proof of SCALE-invariance dominance of economics' capital-markets so-called "complexity", as nothing else! (Anderson-Mandell-Pascual-Leone identically in nerves/brain/mind); FDA.applications: drug testing verification/qualification;... Digits['1,...,9] =(upon Benford-law algrbraic-inversion)= Bosons with d = 0 BEC(!!!), and denominator-EXPONENTIAL Taylor/power-series expansion to Zipf-law Hyperbolicity (Archimedes)INEVITABILITY!!!
Author Bio
BS-Physics/Mineralogy-Colorado School of Mines/CCNY(1965) Attended: Harvard/MIT, University of Pennsylvania MS-Mathematical-Physics, Courant Institute/NYU(1967) PhD-Radiation/Nuclear-Physics, U.C.Berkely(1968) MS-Nuclear-Physics- University of Michigan(1969) PhD-"Metallurgy"/Solid-State Theory/Condensed-Matter Theory/Magnetism, MSU(1970) Industry: AMRAC, Ford, GM, Westinghouse, PSEG, IAEA, ABB,... Teaching: QMUL/Uiversity of London, CUNY, ITB(Bandung, Java,Indonesia), Brazil(CNPq), ICTP/SISSA First Prover of: Fermat's Last-Theorem(FLT) [@ CCNY IN 15-MINUTES(1964), 3-decades