Law of Motion F - PDF document

1 Law of Motion F = ma Dynamics UniformA
Law of Motion F = ma Dynamics UniformAcceleration/Deceleration Equivalence to P(w) =“1”/w “Noise” InverseProportionality Power-Law Decay PowerSpectrum Algebraicity Critical : (So-Called) “Self-Criticality” Is Simply a “Somewhat Tardy” Computer-Rediscovery/Restatement of Newton’s- Edward Siegel (“physical-mathematicist”) (a. k. a. Herr Doktor Professor “Sigmund Frud “FUZZYICS Ó @ Pacific Beach Institute of Simplicity of Complexity Optimality (PBISCO), @ La Jolla Institute of Simplicity of Complexity Optimality (LJISCO) @ La Jolla Institute for Biochemopsychotechnoinformaticsoscientifico(so called)”complexity”...-Babble Spin-Doctoring Media-Hype P.-R. Disambiguation (LaJ-B...A...D) 1101 Hornblende, San Diego, CA. 92109 & 6333 La Jolla Blvd., La Jolla, CA. 92037 (858) 270- fuzzyics@tnl- Much self-touted/promoted so-called “self-criticality” “specificity-complexity

2 48; (SOC)-tactics is simply/merely compu
48; (SOC)-tactics is simply/merely computerrediscovery/restatement of Newton’s-law of motion F : Proof: (1) F rewritten as originally a defines Output/Input c inverse-mass mechanical-susceptibility [definition]; (2) c”) [fluctuation-dissipation theorem]; (3) E=m×) [special-relativity medium maximal-speed]; (4) E=(h [quantum classical-average].Via (3) and (4) m. Inverting: (1/m)»). But by (1): (1/m)ºc). And by (2): c).Thus configuration-(r space F (uniform = translational/invariance) equivalence to dual-( -space integral-transform P(w) =“1”/w “noise” inverseproportionality power-law decay powerspectrum algebraicity Critical ! QED FIN INEVITABILITY RootCause Ultimate-Origin for Newton’s Law of Motion r r F m a 1........ Dominance of Classical-Mechanics Dynamics: DIGIT “NeWBeKLaw” BoseEinstein Condensation to 1.000... Causes “Maxwell-Boltzmann Condensation” RigidBody Dynamics Manifestdemonstrated succinctly with PARSIMONY is the re for the rootcause ultimate- for Newton’s law of motion dominance of classical-mechanics rigid-body dynamics r r F IDEALIZED ABSTRACTION TO r r F m a = × : AVERAGES ’ “Boltzmann classical-statistics ‘CONDENSATION’” with extensions to quantum-theory and quantumtheories, is in automatic BoseEinstein CONDENSATION of DIGITS’ intrinsic/inherent onaverage statistical Newcombe[Am. J. Math., 4, 39 (18 -Goett. Nachr. (1914 ; Math. Ann. 77, 33 (1916 ]-Proc. Am. Phil. Soc. 78, 551 (19 ]- “law Pd)+èçöø÷1 interdigit repulsive- root-cause ultimateorigin for critical-exponents’ DICHOTOMY: n = 0 vs. n = 1.000 INEVITABILITY of asymptotic-limit antipodes of “FUZZYICS ” Synergetics Paradigm & Dichotomy “INEVITABILITY_ ”: with INVERSION to only BoseEinstein quantum-statistics "") 10 1 and EXPANSION to so-called "".. inverseproportionality “noise” (fluctuationdissipation theorem) equivalence to generalized-susceptibility power-spectrum INEVITABIL : () ] ")".."...1011

3 1111000PP=@-@-+++@ with dual Bose-Einste
1111000PP=@-@-+++@ with dual Bose-Einstein CONDENSATION “possibility”(ies): (in addition to numerator/amplitude/ magnitude-limit lim)#...® @ 1 P ) possibilities: at d = 1 for “NeWBeK” first-digit logarithmic-law vs. at d = 0 for any/all-subsequent significant-digit laws, so that most-probable criticalexponent must be n = 1.000... , i.e. to a SELF-FULFILLING/FULFILLMENT “PROPHESY”: r r r r Fb======00010001....................... linearproportionality INEVITABILITY versus r r r r Fb¹¹¹¹¹¹00010001....................... any other possible nonlinear-proportionality impossibility RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r INEVITABILITY RootCause Ultimate-Origin for Newton’s Law of Motion r r F m a 1........ Dominance of Classical-Mechanics Dynamics: DIGIT “NeWBeKLaw” BoseEinstein Condensation to 1.000... Causes “Maxwell-Boltzmann Condensation” RigidBody Dynamics Manifestdemonstrated succinctly with PARSIMONY is the reason for the rootcause ultimate- for Newton’s law of motion dominance of classical-mechanics rigid-body dynamics r r F IDEALIZED ABSTRACTION TO r r F m a = × : AVERAGES ’ “Boltzmann classical-statistics ‘CONDENSATION’” with extensions to quantum-theory and quantumtheories, is in automatic BoseEinstein CONDENSATION of DIGITS’ intrinsic/inherent onaverage statistical Newcombe[Am. J. Math., 4, 39 (18 -Goett. Nachr. (1914 ; Math. Ann. 77, 33 (1916 ]-Proc. Am. Phil. Soc. 78, 551 (19 ]- “law Pd)+èçöø÷1 interdigit repulsive- root-cause ultimateorigin for critical-exponents’ DICHOTOMY: n = 0 vs. n = 1.000 INEVITABILITY of asymptotic-limit antipodes of “FUZZYICS ” Synergetics Paradigm & Dichotomy “INEVITABILITY_ ”: with INVERSION to only BoseEinstein quantum-statistics "") 10 1 and EXPANSION to so-called "".. inverseproportionality “noise” (fluctuationdissipation theorem) equivalence to gen

4 eralized-susceptibility power-spectrum I
eralized-susceptibility power-spectrum INEVITABILITY : () ] ")".."...10111111000PP=@-@-+++@ with dual Bose-Einstein CONDENSATION “possibility”(ies): (in addition to numerator/amplitude/ magnitude-limit lim)#...® @ 1 P ) possibilities: at d = 1 for “NeWBeK” first-digit logarithmic-law vs. at d = 0 for any/all-subsequent significant-digit laws, so that most-probable criticalexponent must be n = 1.000... , i.e. to a SELF-FULFILLING/FULFILLMENT “PROPHESY”: r r r r Fb======00010001....................... linearproportionality INEVITABILITY versus r r r r Fb¹¹¹¹¹¹00010001....................... any other possible nonlinear-proportionality impossibility RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r INEVITABILITY of ""... INVERSEProportionality Unique PowerLaw So-Called “Noise” Power-Spectrum Unique Critical-Exponent n = 1.000... Root-Cause Ultimate-Origin in DIGITS’ Classic (But Decidedly Not Classical!) Pure-Mathematics Newcombe(1881--) InterDigit On-Average Statistical- “NeWBeK Sequence: Pd)+èçöø÷1,... INVERSIONS ALL to Bose-Einstein Quantum-Statistics With Bose-Einstein CONDENSATION to MostProbable (but Not “the Only” Possible) Critical-Exponent n = 1.000... [In Turn The Root-Cause Ultimate-Origin for the INEVITABILITY of Newton’s Law of Motion r r F m a 1........ Dominance of Classicalics Dynamics: DIGIT “NeWBeKLaw” BoseEinstein Condensation to 1.000... Causes “Maxwell-Boltzmann Condensation” Rigid-Body Dynamics] INEVITABILITY of ""... INVERSEproportionality unique powerlaw so-called “noise” equivalence to generalized-susceptibility power-spectrum with unique (most probable out of all possible, but not “the only” possible) critical-exponent_ n= 1.000... root-cause ultimate-origin is manifestly-demonstrated to be in DIGITS’ pure-mathematics classic (but decidedly not classical) Newcombe

5 (1881--) interdigit on-average statistic
(1881--) interdigit on-average statistical- (“odds of gambling”) [Hill-proven to have its rootcause ultimate-origin in: logarithm - invariance = unitsinvariance = SCALE!!!] “NeWBeK sequence: Pd)11-=+èçöø÷, d Î [1 ,2,3,4,5,6,7,8,9]; () )111019-=++èçöø÷, d Î [0 , 1, 2,3,4,5,6,7,8,9]; ...; {} bdiiii-=èçöø÷+èçöø÷éëêêêêùûúúúú=--=)11, d Î [0 , 1,2,3,4,5,6,7,8,9] INVERSION ALL to only BoseEinstein quantumstatistics with Bose-Einstein CONDENSATION to most critical-exponent_ n = 1.000... [which in turn is the root-cause ultimate-origin for the INEVITABILITY rootcause ultimate-origin for Newton’s Law of Motion r r F m a 1........ dominance of classical-mechanics rigid-body dynamics “Maxwell-Boltzmann ‘Condensation’”: DIGIT “NeWBeKlaw” BoseEinstein Condensation to 1.000... causes “Maxwell-Boltzmann Condensation” rigid-body dynamics classical- INEVITABILITY manifestdemonstration of root-cause ultimate-origin for “FUZZYICS ” S.P.D. “Inevitability_ ” so-called “noise” (fluctuation-dissipation theorem-equivalence to) generalized-susceptibility power-spectrum unique critical-exponents’ Dichotomy: n = 0= 0.000... WHITE/FLAT/ FUNCTIONLESS vs. n = 1.000... power-Law Decay HYPERBOLICITY Shlesinger- as DIGITS’ Bose-Einstein CONDENSATION INEVITABILITY to most-probable Digit-sequence in/via 1.000... DIGITS’ onaverage statistical Newcombe(18-- “s Sequence d)+èçöø÷1digit repulsive- root-cause ultimate-origin for critical-exponents’ DICHOTOMY: n = 0 vs. n = 1.000 INEVITABILITY of asymptotic-limit antipodes of “FUZZYICS ” Synergetics Paradigm & Dichotomy “ with INVERSION to Only BoseEinstein Quantum-Statistics "") 10 1 and EXPANSION () ] ")".."...10111111000PP=@-@-+++@ with dual Bose-Einstein CONDENSATION “possibility”(ies): (in addition to numerator/amplitude/magnitude-limit lim)#...® @ 1 P ) possibility at d = 0, so that most-probable critical

6 -exponent is n = 1.000... , i.e. to a
-exponent is n = 1.000... , i.e. to a SELF-FULFILLING/FULFILLMENT “PROPHESY” RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r INEVITABILITY RootCause Ultimate-Origin for Newton’s Law of Motion r r F m a 1........ Dominance of Classical-Mechanics Dynamics: DIGIT “NeWBeKLaw” BoseEinstein Condensation to 1.000... Causes “Maxwell-Boltzmann Condensation” Manifestdemonstration for the rootcause ultimate- for Newton’s law of motion dominance of classical-mechanics rigid-body dynamics r r F IDEALIZED ABSTRACTION TO r r F m a = × : AVERAGES ’ “MaxwellBoltzmann classical-statistics ‘CONDENSATION’” with extensions to quantum-theory and quantum-theories, is in automatic BoseEinstein COND of DIGITS’ intrinsic/inherent onaverage statistical Newcombe[Am. J. Math., 4, 39 (18 -Goett. Nachr. (1914 ; Math. Ann. 77, 33 (1916 ]-Proc. Am. Phil. Soc. 78, 551 (1938 ]- “law Pd)+èçöø÷1 interdigit repulsive- root-cause ultimate-origin for critical-exponents’ DICHOTOMY: n = 0 vs. n = 1.000 INEVITABILITY of asymptotic-limit antipodes of “FUZZYICS ” Synergetics Paradigm & Dichotomy “ ”: with INVERSION to only BoseEinstein quantum-statistics "") 10 1 and EXPANSION to so-called "".. inverseproportionality “noise” (fluctuation-dissipation theorem) equivalence to generalizedsusceptibility power-spectrum INEVITABILITY : () ] ")".."...10111111000PP=@-@-+++@ with dual Bose-Einstein CONDENSATION “possibility”(ies): (in addition to numerator/amplitude/ magnitude-limit lim)#...® @ 1 P ) possibilities: at d = 1 for “NeWBeK” first-digit logarithmic-law vs. at d = 0 for any/all subsequent significant-digit laws, so that most-probable criticalexponent must be n = 1.000... , i.e. [via Siegel manifest-demonstration of r r F m a = × equivalence to P)".. w : (1) r r r====--1, [Definition]; (2) c w w (" " ) ~ (" " ) P [FluctuationDissipation Theorem];

7 47;the Max & Al Show”: (3) E m ~
47;the Max & Al Show”: (3) E m ~ [Special-Relativity: Existence of Upper Limiting-Speed in a Medium: Eº2 ] ; (4) to a SELF-FULFILLING/FULFILLMENT “PROPHESY”: r r r r Fb======00010001....................... linearproportionality INEVITABILITY versus r r r r Fb¹¹¹¹¹¹00010001....................... any other possible nonlinearproportionality impossibility!!!: i.e. RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r INEVITABILITY RootCause Ultimate-Origin for Newton’s Law of Motion r r F m a 1........ Dominance of Classical-Mechanics Dynamics: DIGIT “NeWBeKLaw” BoseEinstein Condensation to (OnAverage) Statistically Most Probable CriticalExponent 1.000... Causes “Maxwell-Boltzmann Condensation” [a.k.a. Rigid-Body Dynamics (1687) Classical- Manifestdemonstration for the rootcause ultimate- for Newton’s law of motion dominance of classical-mechanics rigid-body dynamics r r F IDEALIZED ABSTRACTION TO r r F m a = × : AVERAGES ’ “MaxwellBoltzmann classical-statistics ‘CONDENSATION’” with extensions to quantum-theory and quantum-theories, is in automati BoseEinstein CONDENSATION of DIGITS’ intrinsic/inherent onaverage statistical Newcombe[Am. J. Math., 4, 39 (18 -Goett. Nachr. (1914 ; Math. Ann. 77, 33 (1916 ]-Proc. Am. Phil. Soc. 78, 551 (1938 ]- “law Pd)+èçöø÷1 interdigit repulsive- root-cause ultimate-origin for critical-exponents’ DICHOTOMY: n = 0 vs. n = 1.000 INEVITABILITY of asymptotic-limit antipodes of “FUZZYICS ” Synergetics Paradigm & Dichotomy “ ”: with INVERSION to only BoseEinstein quantum-statistics "") 10 1 and EXPANSION to so-called "".. inverseproportionality “noise” (fluctuation-dissipation theorem) equivalence to generalizedsusceptibility power-spectrum INEVITABILITY : () ] ")".."...10111111000PP=@-@-+++@ with dual Bose-Eins

8 tein CONDENSATION “possibility”
tein CONDENSATION “possibility”(ies): (in addition to numerator/amplitude/ magnitude-limit lim)#...® @ 1 P ) possibilities: at d = 1 for “NeWBeK” first-digit logarithmic-law vs. at d = 0 for any/all subsequent significant-digit laws, so that most-probable criticalexponent must be n = 1.000... , i.e. [via Siegel manifest-demonstration of r r F m a = × equivalence to P)".. w : (A) physics : (1) rr r r====--1, [Definition]; (2) c w w (" " ) ~ (" " ) P [FluctuationDissipation Theorem]; “the Max & Al Show”: (3) E m ~ [Special-Relativity: Existence of Upper Limiting-Speed in a Medium: Eº2 ] ; (4) E ~ w [proportionality: not (necessarily)”the quantum”]. By (3) & (4): m E ~ ~ w . Inverting: 111 ~ . But by (1) and (2): P E ))~ w 11. Hence r r F m a = × equivalence to P)".. w ! , in agreement with (B) pure : r r F m a = × double time-integral range-formula uniform r r r r r r sao= time formal integraltransform (Fourier, Laplace, z,...) to a formal power is: [] } aatataittit)((()(())".....wwww¹=¹+¹==--=+¹º--¥òòrrrrrrrrrrrr2200122000121000 to a SELFFULFILLING/FULFILLMENT “PROPHESY”: r r r r Fb======00010001....................... linearproportionality INEVITABILITY versus r r r r Fb¹¹¹¹¹¹00010001....................... any other possible nonlinear-proportionality impossibility RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r Newton’sLaw of Motion F = ma Both Different Physics and Pure-Mathematics Yet Equivalent Manifest-Demonstration Equivalence to FluctuationDissipation Theorem Equivalent “1”/w Generalized-Called) “Noise” Power-Spectrum INEVITABILITY : (1667) F = ma Was Merely Accidental Rediscovery in (So-Called) “Self-Criticality” (SOC) “SpecificityComplexity” (SoC-tactics)!: Brillouinization /

9 Fourier- of Newton’s Law of Motion
Fourier- of Newton’s Law of Motion Classical- “FUZZYICS”’ SYNERGETICS PARADIGM & DICHOTOMY “INEVITABILITY_-WEB” OUTLINE Siegel S.P.D. “FUZZYICS ” automatically with optimality is, in list- SYNERGETICS PARADIGM & DICHOTOMY(SPD) “COMMON” PARSIMONYDICHOTOMY (POD)- DIMENSIONALITY (DD)- INEVITABILITY ROOT-CAUSE ULTIMATE- ( 0.) DIMENSIONALITY DEGREES LEVEL0. LOGIC : df = dst = ODD AUTMATHCAT - - - - - - - - - - -� CROSSOVER via INTERMEDIATE CONTINUOUS INTERPOLATING FRACTIONAL FRACTAL- EVEN INTEGER = dst =d-f DIMENSIONALITY UN FLUCTUATIONS = ODD Z Dst EVEN Z = dst cau ß ses cau ß ses cau ß ses ( I.) EXTENT/ LEVELI. LOGIC : (relative (relative [BOUNDARYFUL]=[LOCALITY] AUTMATHCAT - - - - - - - - - - -� CROSSOVER (...GLOBALITY...)=(...BOUNDARY ...) {Kallen &/|| &/|| representation (II.) POWER LEVELII. LOGIC : [“l”/WHITE/ FLAT/FUNCTION AUTMATHCAT - - - - - - - - - - - -� CROSSOVER (...”l”/w HYPERBOLICITY ...) whose frequency defines at least necessarycondition for so-called “complexity” as Noether’s-theorem SCALE current

10 4- / (d/d ) [[ ¶ = 0] ( w)] = 1/ w =
4- / (d/d ) [[ ¶ = 0] ( w)] = 1/ w =(for arbitrary base)= “1”/ w &/|| &/|| (III.) CRITICAL LEVELIII. LOGIC : n = 0 AUTMATHCAT - - - - - - - - - - -� CROSSOVER n = 1.000... Ý ß Ý ß Ý ß DIMENSIONALITY DEGREES-FREEDOM - IN ALSO ROOT-CAUSE ULTIMATE- (IV.) NOETHER'S - THEOREM : CONTINUOUS- S C A L E- SYMMETRY LEVELIV. LOGIC : SCALE - INVARIANCE SYMMETRY - RESTORING � SCALE - INVARIANCE SYMMETRY - BREAKING Ý causes ß Ý causes ß Ý causes ß ¶ = 0 SCALE 4-[VERGENCE] 4-[ whose frequency- defines at least necessaryion for so-called “complexity” as Noether’stheorem SCALE current 4-/ CONSERVATION (d/d ) [[ ¶ = 0] ( w)] = 1/ w =(for arbitrary base)= “1”/ w � 0 ¹ ¶ SCALE 4-(... DIVERGENCE...) 4 & & & DIMENSIONALITY DEGREES-FREEDOM - IN ALSO ROOT-CAUSE ULTIMATE- (V.) STAR}

11 OF OTHER NOETHER'S
OF OTHER NOETHER'S - THEOREM: CONTINUOUS SYMMETR LEVEL : . . . - INVARIANCES SYMMETRY - RESTORING - � . . . - INVARIANCES SYMMETRY - BREAKING - Ý causes ß Ý causes ß Ý causes ß { ... = 0}- { . . . { { � {0 ¹ ¶ ... { . . . {(... DIVERGENCES { [fluctuationdissipation theorem-equivalent] noise @ generalized-susceptibility [c) = d(OUTPUT)/d(INPUT) = d(EFFECT or RESULT)/d(CAUSE)] power-spectrum qualitative-type functional-form and quantitative critical-exponent "automatic- mathematicalcatastrophe" (AUTMATHCAT) "dimensionality-catastrophe" (DIM-CAT) crossover second-order phase-transition critical-phenomenon. [the Kallen-Lehmann representation-equivalence, reviewed succinctly by Bjorken & Drell, are that extant measures of asymptoticlimit antipodes of the PARSIMONY-Dichotomy (relative) [LOCALITY] = [BOUNDARYFUL] versus (relative) (...BOUNDARYLESS...) = (...GLOBALITY...): propagators @ Green's-functions @ diffusivity @ ... are equivalent to extant measures of asymptotic-limit antipodes of the PARSIMONY-Dichotomy (relative) ["l"/wWHITE/FLAT/FUNCTIONLESS] versus (relative) (..."1"/w FLICKER HYPERBOLICITY ...): {fluctuation-dissipation theoremequivalent} noise @ generalized-susceptibility power-spectrum as complex-functions of complex-variable w'+i w" in first even-integer critical-dimensionality complex-plane C in their pure-mathematics analyticity ]. For purposes of (so-called) “Bak” “self-criticality” (“SOC

12 ”) “specificity-complexity
”) “specificity-complexity” (SoC)-tactics merely being an “accidental” rediscovery of 1687 Newton’s-law of motion F = ma , original Siegel12 manifest-demonstration, in list- SYNERGETICS PARADIGM & DICHOTOMY(SPD) “COMMON” PARSIMONYDICHOTOMY (POD)- DIMENSIONALITY (DD)- INEVITABILITY ROOT-CAUSE ULTIMATE- ( 0.) DIMENSIONALITY DEGREES LEVEL0. LOGIC : df = dst = ODD AUTMATHCAT - - - - - - - - - - -� CROSSOVER via INTERMEDIATE CONTINUOUS INTERPOLATING FRACTIONAL FRACTAL DIMENSIONALITY UN FLUCTUATIONS = ODD Z Dst EVEN Z = dst EVEN INTEGER = dst =d-f cau ß ses cau ß ses cau ß ses ( I.) EXTENT/ LEVELI. LOGIC : (relative (relative [BOUNDARYFUL]=[LOCALITY] AUTMATHCAT - - - - - - - - - - -� CROSSOVER (...GLOBALITY...)=(...BOUNDARY ...) III III III [UNIFORM/CONSTANT VELOCITY] - (...UNIFORM/CONSTANT III III III {Kallen &/|| &/|| representation (II.) POWER LEVELII. LOGIC : (in TWO “distinct” WAYS : · (1) “pure” &/or/ · (2) “pure”- ________________________ · (1) “pure” (expanded in size below table for clarity!!

13 ) ()()[]()()()[]()"]()"()()11234534 rrr
) ()()[]()()()[]()"]()"()()11234534 rrr-=èçöø÷èçöø÷ºººººº--@-=--=cwww P~))()())]()).......1161111271èçöø÷æèçöø÷æèçöø÷æèçöø÷ºèçöø÷èçöø÷èçöø÷-èçöø÷wwwwwrrr &/or/ &/or/ · (2) “pure”- [] ] rrrrrrrrrraat--=+------ºº=+==-¹==+¹ò)()))()()()((122012200012 ] ] ] ))()(()[]()....".....=---==èçöø÷èçöø÷=+¹=-++-ºº-®at00022001221w¶¶wwrr III III III [] )()()()[]w===- 0 + [] [ ] at)()(().......w=¹==-221 III III III [“l”/WHITE/ FLAT/FUNCTION AUTMATHCAT - - - - - - - - - - - -� CROSSOVER (...”l”/w HYPERBOLICITY ...) whose frequency defines at least necessary condition for so-called “complexity” as Noether’s- theorem SCALE current 4- / (d/d ) [[ ¶ = 0] ( w)] = 1/ w =(for arbitrary base)= “1”/ w &/|| &/II &/|| (III.) CRITICAL LEVELIII. LOGIC : n = 0 AUTMATHCAT - - - - - - - - - - -� CROSSOVER n = 1.000... Ý ß Ý ß Ý ß DIMENSIONALITY DEGREES-FREEDOM - IN ALSO ROOT-CAUSE ULTIMATE- (IV.) NOETHER'S - THEOREM : CONTINUOUS- S C A L E- SYMMETRY LEVELIV. LOGIC : SCALE - INVARIANCE SYMMETRY - RESTORING � SC - INVARIANCE SYMMETRY - BREAKING Ý

14 causes ß Ý
causes ß Ý causes ß Ý causes ß ¶ = 0 SCALE 4-[VERGENCE] 4-[ whose frequency- defines at least necessarycondition for so-called “complexity” as � 0 ¹ ¶ SCALE 4-(... DIVERGENCE...) 4 Noether’stheorem SCALE current 4-/ CONSERVATION (d/d ) [[ ¶ = 0] ( w)] = 1/ w =(for arbitrary base)= “1”/ w & & & DIMENSIONALITY DEGREES-FREEDOM - IN ALSO ROOT-CAUSE ULTIMATE- (V.) STAR} OF OTHER NOETHER'S - THEOREM: CONTINUOUS SYMMETR LEVEL : . . . - INVARIANCES SYMMETRY - RESTORING - � . . . - INVARIANCES SYMMETRY - BREAKING - Ý causes ß Ý causes ß Ý causes ß { ... = 0}- { . . . { { � {0 ¹ ¶ ... { . . . {(... DIVERGENCES { ________________________ ________________________: ______________________________: III III III TRANSLATIONAL - INVARIANCE SYMMETRY - RESTORING - � TRANSLATIONAL - INVARIANCE SYMMETRY - BREAKING -

15 Ý
Ý causes ß Ý causes ß Ý causes ß {0 = ¶ TRANSLATIONAL { TRANSLATIONAL 4- 4- [CONSERVATION] � {0 ¹ ¶ TRANSLATIONAL { TRANSLATIONAL 4- NON- {(... DIVERGENCE...)} { { { & & & ROTATIONAL - INVARIANCE SYMMETRY - RESTORING � ROTATIONAL - INVARIANCE SYMMETRY - BREAKING Ý causes ß Ý causes ß Ý causes ß {0 = ¶ ROTATIONAL { ROTATIONAL 4- 4- [CONSERVATION] { { � {0 ¹ ¶ ROTATIONAL { ROTATIONAL 4- NON- {(... DIVERGENCE...)} { [fluctuationdissipation theorem-equivalent] noise @ generalized-susceptibility [c) = d(OUTPUT)/d(INPUT) = d(EFFECT or RESULT)/d(CAUSE)] power-spectrum qualitative-type functional-form and quantitative critical-exponent "automatic-catastrophe" (AUTMATHCAT) "dimensionality-catastrophe" (DIM-CAT) crossover second-order phase-transition critical-phenomenon. [the Kallen-Lehmann representation-equivalence, reviewed succinctly by Bjorken & Drell, are that extant measures of asymptoticlimit antipodes of the PARSIMONY-Dichotomy (relative) [LOCALITY] = [BOUNDARYFUL] versus (relative) (...BOUNDARYLESS...) = (...GLOBALITY...): propagators @ Green's-functions @ diffusivity @ ... are equivalent to extant measures of asymptotic-limit antipodes of the PARSIMONY-Dichotomy (relative) ["l"/wWHITE/FLAT/FUNCTIONLESS] versus (relative) (..."1"/w FLICKER HYPERBOLICITY ...): {fluctuation-dissipation theorem-equivalent} noise @ generalizedsusceptibility power-spectrum as complex-functions of complex-variable w'+i w" in first even-integer criti

16 cal-dimensionality complex-plane C in th
cal-dimensionality complex-plane C in their pure-mathematics analyticity ]. i. e.: (1): ()()[)()()[]()"]()"()()11234534 rrr-=èçöø÷èçöø÷ºººººº--@-=--=cwww P ~))()())]()) .......1161111271èçöø÷æèçöø÷æèçöø÷æèçöø÷ºèçöø÷èçöø÷èçöø÷-èçöø÷wwwwwrrr and/“versus”: (2) [][] rrrrrrrrrraat--=+------º=+==-¹==+¹ò)()))()()()((122012200012 ] ] ] =---==èçöø÷èçöø÷=+¹=-++-ºº-®at00022001221))()(()[]()....".....w¶¶wwrr i. e.: [] )()()()[]w===- 0 + [] [ ] at)()(().......w=¹==-221 Thus, all Bak’s SOC SoC-tactics have done is to “accidentally” rediscover the (1667) Newton’s-law of motion F = ma some 320 years later!!! RIGID BODY DYNAMICS F m a CLASSICAL MECHANICS - = - º r r "'""....."-=--000r 1. E. Siegel: Symposium on Fractals, Scaling,... , M.R.S. Fall Mtg., Boston (1989-summary!; ibid. (1990)-2!; I. B. M. Conf. On Computers and Mathematics , Stanford (1986); J. Noncryst. Sol. 40, 453 (1980); Aristotle Birthday Symposium on Mechanics and Physics , Thessoloniki (1990); ... 2. M. Shlesinger and B. West, Intl. J. Mod. Phys. ??? (1989);... 3. P. Handel, Phys. Rev. A22, 2, 745 (1980);... 4. K.-L. Ngai, Comments in Solid-State Physics: 9, 4, 127 (1979); 9, 5, 141 (1980);... 5. Y. Klimontovich, J.E.T.P. Lett. 51, 51 (1990); Statistical , Pitman (1978);... 6. R. Horsthemke and R. Lefever, NoiseInduced Phase- , Springer(1983), (1987) 7. F. McClintock and F. Moss, Noise in Physical- , Addison-Wesley (1989?) 8. M.-O. Hongler, Chaotic and Stochastic Behavior of Automated Manufacturing- , Spring

17 er (1992) 9. Y. Bar-Yam, Dynamics of Co
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