1 !! DON'T PANIC !! -Adams (HHGG) 2 The spectacular physical application of Clifford algebra is the Dirac equation. -- Finkelstein 3 It is only the very wisest and the very stupidest who cannot change. -- Confucius 4 To have faults and to be making no effort to correct them is to have faults indeed. -- Confucius 5 The demands that good people make are upon themselves; those that bad people make are upon others. -- Confucius 6 Never do to others what you would not like them to do to you. __ Confucius 7 One who will not worry about what is far off will soon find something worse than worry close at hand. -- Confucius 8 Good people are ashamed to let their words outrun their deeds. -- Confucius 9 If I hold up one corner and a student cannot come back to me with the other three, I do not continue the lesson. -- Confucius 10 Be slow in word but prompt in deed. -- Confucius 11 Good people take as much trouble to discover what is right as bad people take to discover what will pay. -- Confucius 12 One who learns but does not think, is lost. One who thinks but does not learn is in great danger. -- Confucius 13 Clever talk and a pretentious manner are seldom found in good people. -- Confucius 14 What satisfies me the most? Basically, that I've never worked for a living. -- Marcel Duchamp 15 Even if I could try a civil suit as well as anyone, it would be better to bring it about that there were no civil suits. -- Confucius 16 Int[V8] ( ( d^2~H8 /\ *d^2H8 + + F8 /\ *F8 + + ~S8± (gamma)d S8± ) + + gg + n'(Dg/DA)dn) 17 You can make a model of anything from the harmonic functions on the unit disk. -- Feller 18 It is more important to have beauty in one's equations than to have them fit experiment. -- Dirac 19 The whole purpose of physics is to find a number, with decimal points, etc! Otherwise you haven't done anything. -- Feynman 20 Another peculiarity of 4-dimensional space is the occurrence of the 24-cell, which stands quite alone. -- Coxeter 21 If you calculate a result that disagrees with experiment, you need courage to say the experiment must be wrong. -- Feynman 22 Good people who hold the left side of a contract do not take unfair advantage. -- Lao Tzu 23 To lead with cleverness brings harm. To lead without cleverness brings benefit. -- Lao Tzu 24 Why is there something instead of nothing? < > enables us to build the world from 0. -- Finkelstein & Rodriguez 25 Maybe other worlds have folks with more advanced brains. Maybe not. Either way, it's a mighty sobering thought. - Kelly (Porkypine and Pogo) 26 I believe that the theory that space is continuous is wrong, because we get infinities and other difficulties. -- Feynman 27 Whenever a creature was faced with several possible courses of action, it took them all, thereby creating many distinct histories of the cosmos. - O.S. 28 Charge is just the ability to make virtual photons, and the electric field is nothing but the virtual photon cloud. -- Gonick and Huffman 29 I believe nobody will read this book for 100 years, but I don't care. -- Kepler, about 100 years before Newton 30 Kepler was a better scientist than Galileo. Galileo did experiments that others might have done. Kepler did things other people would not do.-E.T. 31 I am One that transforms into Two. I am Two that transforms into Four. I am Four that transforms into Eight. After this I am One again. -- Hermopolitan creation myth (quoted by Schneider) 32 There are two camps in the current world. In one camp the common good is sought for the masses, while the other camp specializes in keeping most of the benefits for the people in the ruling class. -- Hua Loo-Keng 33 A mathematician has to be judged by his research accomplishments and not by the number of university degrees earned. -- Wang Yuan in his book "Hua Loo-Keng" 34 The death of Zhou Enlai in 1976 was marked by Comet West. The death of Deng Xiaoping in 1997 was marked by Comet Hale-Bopp. 35 If some years were added to my life, I would give fifty to the study of I Ching, and then I might come to be without great faults. -- Confucius 36 A thorough advocate in a just cause, a penetrating mathematician facing the starry heavens, both alike bear the semblance of divinity. - G. 37 Wagner was a wonderful sunset that had been mistaken for a dawn. -- Debussy 38 Life computers can reproduce! -- Conway and Guy 39 "Beauty is truth, truth beauty", -- that is all Ye know on earth, and all ye need to know. -- Keats 40 I believe that all things are fundamentally interconnected, but some things are a great deal more interconnected than others. - Adams (Gently) 41 Music has no meaning or purpose other than to be itself. -- Adams (MacDuff) 42 42: The Tao produced the One. The One produced the Two. The Two produced the Three. The Three produced All things. -- Lao Tzu 1=unity,2=duality,3=the rest. -- Marcel Duchamp 43 The laws of physics will turn out to be simple, like the checkerboard with all its apparent complexities. -- Feynman 44 1 8 28 56 70 56 28 8 1 S8 Spin(8) ____________________ 256 = 16 x 16 = 4 x 8x8 2x(gamma)8 OP2 45 F4-AutGroup a O+ Ov triality: ~O+ b O- Spin(8):O+ -> xO+ ~Ov ~O- c Spin(8):Ov -> xOvx Spin(8):O- -> O-x 46 Quantization of the conformal degree of freedom leads to a consistent and reasonably complete picture of maximally symmetric spacetime.- N.and P. 47 <1,i,j,k,e,ie,je,ke>---><1,i,j,k> O: _ OxO: /| or |\ OxOxO: | | 48 War is hell. -- Sherman 49 If nominated I will not run. If elected I will not serve. -- Sherman 50 F4 = Aut(H3(O)) __________________ H3(O) <-> E7/E6xU(1) Rdim27 Cdim27 (CxO)P2s in (HxO)P2 51 Spin(9) -> F4 -> OP2 __________________ OP2 <-> E6/Spin(10)xU(1) Rdim16 Cdim16 (CxO)P2 52 Spin(8) -> Spin(9) -> S8 S8 <-> Spin(10)/Spin(8)xU(1) Rdim8 Cdim8 RP1s in RP9 ______Silovbdy=RP1xS7____ 53 F4 = Aut(H3(O)) _________________ E6 = F4 + H3(O)0xS1 E7 = F4 + H3(O)0xS3 + SU(2) E8 = F4 + H3(O)0xS7 + G2 54 OP2 = F4/Spin(9) (CxO)P2 = E6/Spin(10)xU(1) (HxO)P2 = E7/Spin(12)xSU(2) (OxO)P2 = E8/Spin(16) __________________ 55 O__OxO__OxOxO nu 1 e e; or 1 rd,bd,gd ie,je,ke; or e or 1 ru,bu,gu i,j,k 56 SU(2) Weak Force S2&endash;S2 2[vol(S2)vol(Q)/(vol(D)^(1/2))] D = Spin(5)/SU(2)xU(1) Q = RP1xS2 57 SU(3) Color Force CP2 vol(CP2)vol(Q)/vol(D)^(1/4)) D = B6 = SU(4)/S(U(3)xU(1)) Q = S5 58 Spin(5) Gravity S4 vol(S4)vol(Q)/(vol(D)^(1/4)) D = Spin(7)/Spin(5)xU(1) Q = RP1xS4 59 U(1) Electromagnetism S1xS1xS1xS1 = T4 4vol(S1) aE = 1/137.03608 60 mW+ + mW- + mW0 = 260 GeV = [aW/aE][4+mf1] = mHiggs mW+ + mW-=[Sqrt(2v(S2))/Sqrt(3(S1))] mZ = mW± + (mW0-mW±)/4rt(6) sin2(theta-w) = 1 - (mW±/mZ)^2 61 mF = v(Q)xN(grv)xN(oct)xSym mt = (483/21)mb = 130 GeV 62 Kobayashi-Maskawa: e = pi / 2 sina = +mf1/Sqrt(+m^2f1++m^2f2) sinb = +mf1/Sqrt(+m^2f1++m^2f3) sing = +mf2/Sqrt(+m^2f2++m^2f3) - - Sqrt(+mf2/+mf1) 63 Radiative: mnue =4mw^2L/g^2Mpl = 2x10^(-6)eV mnumu =[mmu/me] mnue = 4x10^(-4)eV mnutau =[mtau/me] mnue = 8x10^(-3)eV MSW consistent with KM 64 G(m^2proton) = 6x10^(-39) GF(m^2proton)=1.02x10^(-5) aC = 0.6286 at 245 MeV; 0.169 at 5.3 GeV; 0.106 at 91 GeV 65 H*(Spin(8);R)=/\(x3,x7,x11,x7') a/g0 = Bg0 = BO8G = O7Spin(8) H*(BRS-a/g0) = S(x0,x0',x4) 66 Mozart is free to create things others cannot imagine, because he is bound by principles others cannot see. -- Boden 67 Far from being the antithesis of creativity, constraints on thinking are what make creativity possible. -- Boden 68 Now, for the first time, we perceive the future as a function of our own actions. -- Bernal (1929) 69 Do not be clever-Axelrod 5) Rat 4) Pavlov 3) Tit for Tat 2) Altruist 1) TURN CHEEK (Remo=>Stable) - Michael Gibbs - Oct 93 70 L I z A R d 71 sxs =1 + F + L in Cl(8) sxs =1 + x3 + C + L in Cl(7) x3(a,b,c)=<ab,c>=Re(axbxc) C=*x3 F(a,b,c,d)=<a,bxcxd> O: axbxc=(1/2)(a(~bc)-c(~ba)) 72 Psychohistory deals with reactions of large human conglomerates to social and economic stimuli. -- Asimov 73 To study the laws of history, we must study the common, infinitesimally small elements that influence the masses. -- Tolstoy 74 Always study law - Not to practice, but to understand the ground rules. -- Heinlein (Long) 75 If it can't be expressed in figures, it is not science; it is opinion. -- Heinlein (Long) 76 It's amazing how much "mature wisdom" resembles being too tired. -- Heinlein (Long) 77 In a mature society, "civil servant" is semantically equal to "civil master". -- Heinlein (Long) 78 It is contradictory to "love nature" and deplore "artificialities" with which "people have despoiled nature". -- Heinlein (Long) 79 Any government will work if authority and responsibility are equal and coordinate. -- Heinlein (Long) 80 What are the facts? You pilot always into an unknown future; facts are your single clue. Get the facts! -- Heinlein (Long) 81 Stupidity cannot be cured with money, or through education, or by legislation. -- Heinlein (Long) 82 Courage is the complement of fear. One who is fearless cannot be courageous, and is also a fool. -- Heinlein (Long) 83 The two highest achievements of the human mind are the twin concepts of "loyalty" and "duty". Without them, a society is doomed. - Heinlein 84 Anyone who cannot cope with mathematics is not fully human. -- Heinlein (Long) 85 Specialization is for insects. -- Heinlein (Long) 86 Do not handicap your children by making their lives easy. -- Heinlein (Long) 87 One person's "magic" is another person's engineering. -- Heinlein (Long) 88 If you are one of the minority who can do creative work, never force an idea. Learn to wait. -- Heinlein (Long) 89 A "critic" is one who creates nothing and thereby feels qualified to judge the work of the creative. -- Heinlein (Long) 90 The difference between science and the fuzzy subjects is that science requires reasoning, while the others require scholarship. - Heinlein 91 Secrecy is the beginning of tyranny. --Heinlein (Long) 92 Deductive logic is tautological; there is no way to get a new truth out of it. -- Heinlein (Long) 93 Natural laws have no pity. -- Heinlein (Long) 94 Sin lies only in hurting other people unecessarily. -- Heinlein (Long) 95 Duty is not what others expect of you; it is what you owe to yourself to fulfill obligations you assume voluntarily. -- Heinlein (Long) 96 Time is your total capital, and the minutes of your life are painfully few. So learn to say NO! -- Heinlein (Long) 97 The human nervous system has already evolved a vast distance beyond biomedical science. -- Thomas 98 Although Western medicine has failed to accept sudden death by stress, the physiology probably involves the CNS. -- Fishman, et. al. 99 Four good deeds of Ogodei: defeated enemies; postal service; irrigation systems; intelligence networks. -Secret History of the Mongols 100 Four wrongs of Ogodei: wine; unprincipled lovers; harming Temujin's servant; fencing wild animals. -Secret History of the Mongols 101 Probability(F) = FF* F - emitter, from past F* - absorber, from future Transactions in Many Worlds -- Cramer; Wolf 102 Time flies like an arrow. Fruit flies like a banana. 103 This sentence is false. 104 UCAG x UCAG x UCAG 4^3 = 64 > 20 amino acids For DNA U->T T<->A C<->G 105 T=100GeV; R=10^14cm: Higgs. T=100MeV; R=10^17cm: hadrons. T=1MeV; R=10^19cm: nu decouple. T=10eV; R=10^24cm: mat=rad. T=0.3eV; R=10^24cm:photons decouple. 106 STAR FORMATION: Magnetic field of collapsing cloud discharged by stellar flares carrying angular momentum to planet nodes. 107 Any system with arithmetic has undecidable algorithms varying randomly as the digits of the halting probability Omega. -- Chaitin 108 The halting probability Omega is incompressible and random. In the infinite oracle limit, Omega is a computable sequence. -- Chaitin 109 Biological evolution = parallel computation with molecular components = the nearest thing to an oracle -- Chaitin 110 Deep Thought's successor = Life on Earth -Adams (HHGG) Biological evolution = the nearest thing to an oracle - Chaitin 111 Omega (halting probability) cannot be computed finitely. -Chaitin The Tao that can be named is not the Tao of the Absolute. - Lao Tzu 112 Infinite Improbability Drive - Finite Probability of being at Any Point of Any Universe. -- Adams (HHGG) 113 Begin with 0=origin <0>=ray to<0> <<0>>=ray to<<0>> <<0>,<<0>>> = superpositions transformed by Spin(2)=>S1,C... ...Spin(N).Triality=>Spin(8);C=>E6 114 S4 k=1 => Spin(4)= =SU(2)xSU(2)=S3xS3 S4 k=2 => Spin(8) S4/\S4 = S8 S8 k=1 => Spin(8)=S7xG2xS7 115 DIAMOND Cubic Semiconductor IndRf: 2.407(red) 2.465(violet) ThermCond: 23.2W/cmK(298K) 116 Indra's Net Cyberspace: Reflecting Jewel at Every Intersection - Benedikt 117 Cyberspace: Representation of All Data of Every Node in the System. --Gibson (Neuromancer) 118 BAMA: Boston-Atlanta Metropolitan Axis. Home of Cowboys: Lupus(Case), Dixie(Flatline,McCoy pauley) --Gibson (Neuromancer) 119 Wintermute + Neuromancer & Kuang ICEbreaker & Zion dub = Cyberspace MATRIX with voice that was MUSIC --Gibson (Neuromancer) 120 MATRIX: I talk to my own kind. There's OTHERS. --Gibson (Neuromancer) 121 The OTHERS gave the MATRIX a SHAPE, an overall total form. --Gibson (Mona Lisa Overdrive) 122 Photonic Cyberspace Net:Dimension determined by bandwidth and sphere-packing codes based on Leech /\24, etc. - see Conway & Sloane 123 PHOTONIC SYSTEMS: Security is a higher-protocol problem, since photonics does not easily control access. -Fiber Optic Networks (Green) 124 OPTICAL FIBRE - 1000 nm; ns tuning time; 10^(-15) ber; 1 milliwatt (10^16 photon/s): 10^4 nodes at 1 Gb/s -Fiber Optic Networks (Green) 125 Laser Space Communication + Nuclear or Anti-Matter Probes | gamma-ray laser Space Comm Net 126 Soliton bits: 10^(-11) s ATOMIC: 1 eV - 1000 nm NUCLEAR gamma: 1 MeV - 10^(-10) cm gamma-ray data rate: 10^6 Gb/s/ch; 10^8 Gb/s/channel with Solitons 127 Human DNA: 10^10 triples of 4 kinds nucleotides, 4x4x4=64 states code for 20 amino acids + 3 stops: log2(20)x10^10 bits = 10^2 Gb Neurons>Axons>Microtubules> >Tubulin>electrons(+/-) 128 Neural Network Learning in the Brain; the Immune System; the Evolutionary System: similar processes on time scales of 10^(-3); 10^5; 10^12 sec. -- Pagels, on Edelman 129 Human Brain: 10^11 neurons, each with 10^4 2-state TubDimers: 10^15 b = 10^6 Gb state of mind. Data rate-nanosec transitions: 10^15 Gb/s 130 gamma-ray bursts: 30 sec duration; lots of millisec substructure; broad spectrum around 1 MeV; 10^26 erg at 10^(-2) l-yr=10^3AU; 2/day. Physics Today Feb 92 131 (1 deg / 360 deg)^2 = 10^(-5) Fission 1 kg 235U = 10^21 erg Annihilation 1 gm = 10^21 erg Solar at earth/day = 10^29 erg Solar Grav Lens focus: 550AU 132 Pd Foil Cold Fusion Generator: 1 cm^3 - 3 kilowatts (0.2 hr) 1 m^3 - 3 gigawatts Antimatter Battery: (1 cm)^3-10^24 GeV-1 megaWyr 133 Particle-Antiparticle Pair Creation: Saddle Node Bifurcation (d^2)F = m^2 - F*F - see Guckenheimer & Holmes 134 Connected Simple Quivers of Arrows: A-D-E Dynkin Diagrams: Lagrangian Singularities. -Catastrophe Theory (Arnold) 135 Coxeter-Dynkin Diagram Identities: A1=B1=C1 B2=C2 D3=A3 D5=E5 136 In 1261 Yang Hui described the binomial triangle that was rediscovered in Europe by Pascal.

137

0 Cl(0) 1 R Tao Cl(1) 1 1 C Tai Ji Cl(2) 1 2 1 Q Yin-Yang, I Ching Cl(3) 1 3 3 1 O 3 Realms, Tai Hsuan Ching Cl(4) 1 4 6 4 1 S 5 Elements Cl(5) 1 5 10 10 5 1 M(4,C) Cl(6) 1 6 15 20 15 6 1 M(8,R), I Ching Cl(7) 1 7 21 35 35 21 7 1 M(8,R)+M(8,R), S7 <x> G2 Cl(8) 1 8 28 56 70 56 28 8 1 M(16,R) D4-D5-E6 Physics 2^8 = 16x16 = 8x8 + 8x8 + 256 128 64 32 16 8 4 2 1 + 8x8 + 8x8 256+1024+1792+1792+1120+448+112+16+1 = 3^8 Tai Hsuan Ching

where:

<x> = twisted (fibration) product, (x) = tensor product, Cl = Clifford Algebra,

R = Real Numbers, C = Complex Numbers, Q = Quaternions, O = Octonions, S = Sedenions, M(n,K) = nxn matrix algebra over the field K.

Cl(8N) = Cl(8) (x)...(N times)...(x) Cl(8) Many-Worlds Quantum Theory Cellular Automata Wei Qi Basins of Attraction interact by Zhen-Shan-Ren

138 SU(n) /\(1) ... /\(n-1) Spin(2n+1) /\(1) ... /\(n-1); D Spin(2n) /\(1) ... /\(n-2); D± Sp(n)(2n) /\(1) ... /\(n) - /\(n-2) 139 G2 7 14[27 64 77 77 182...] F4 26 52=28+8+16 273 1274 E6 27 78=28+16+1+32+1 351 2925... E7 56 133 912 1539 8645... E8 248=120+128 3875... 140 Jordan Algebra: (1/2)(AB+BA) F ->A-> FA ->B-> (FA)B =/= F(AB) F ->B-> FB ->A-> (FB)A =/= F(BA) F ->(AB+BA)/2-> F((AB+BA)/2) => Sum Over Histories 141 Iron when heated glows: red to yellow to blue. Classical Physics was wrong, Cooks and Blacksmiths knew. - Gottfreid and Weisskopf 142 Lattice Spacetime Lightcones: 2d:(±1±i)/Sqrt2 : c = 1 4d:(±1±i±j±k)/2 : c = Sqrt3 8d:(±1±i±j±k±e±ie±je±ke)/2Sqrt2: c = Sqrt7 143 Beings woven from light would live "nowhere" and "nowhen". - Manin Quantum Sum Over Histories gives Universe of all possible "crystals" of worldlines. 144 e ^ i pi = -1 145 Music is the Mathematics of Sense. Mathematics is the Music of Reason. - Sylvester 146 Kepler's Platonic Mysticism- Irrational equations of the lowest order - Least rational - Least affected by resonance. -- Thirring (re KAM) 147 Human Brain Waves are 1 to 30 Hz, in tune with the Earth's Schumann Resonances. Dolphin Brains look like Double Brains. 148 HilbertBilinearJordanQuadratic |a> |a><a|=Pa Pa H|a> Hoa Pr(H)Pa=<HPaH> <a|H|a> TrHoPa Tr<PaHPa> [H,H'] ? 4(Pr(H)oPr(H')-Pr(HoH')) 149 HilbertBilinearJordanQuadratic <a|H|b> ? ? |<a|H|b>|^2 TrPe(Pa)Pr(H)Pš) PaoTr<HPbH> 150 Conformal: E7 (complexify) J3(O) E6xU(1) J3(O) M12(O) Spin(10)xU(1) M12(O) J(G7) Spin(8)xU(1) J(G7) SpCnf Lor U(1) Trnsl 151 I hear and I forget. I see and I remember. I do and I understand. 152 n Cl(n) PI(n)(O) PI(n)(Sp) Clc(n) PI(n)(U) 7=-1 R+R Z Z C+C Z 0 R Z/2 0 C 0 1 C Z/2 0 C+C Z 2 Q 0 0 C 0 3 Q+Q Z Z C+C Z 4 Q 0 Z/2 C 0 5 C 0 Z/2 C+C Z 6 R 0 0 C 0 153 32-d complex spinors: E6/Spin(10)xU(1)=(CxO)P2 16-d complex spacetime: Spin(10)/Spin(8)xU(1)=(CxO)P1 28-d Gauge group: Spin(8) 154 A-D-E: (An - n-polygon) Dn - n,2,2 - n-dihedra E6 - 3,3,2 - tetrahedron E7 - 4,3,2 - cube E8 - 5,3,2 - dodecahedron 155 3- dim Schlafli Double-Six: 27 = 6+6+15 lines on cubic 72 sets of 6 disjoint lines 156 2- dim quartic: 28 bitangents 157 6-dim E6 root vectors: 40 perm of (±2,±2,0,0,0;0) and 32 points (±1,±1,±1,±1,±1;±Sqrt3) (with odd no. of - signs) 158 6-dim E6 root lattice: 27 nearest to (0,0,0,0,0,4Sqrt3): (0,0,0,0,0,0) +10 perm of (±2,0,0,0,0;2Sqrt3) +16(±1,±1,±1,±1,±1;Sqrt3) (odd-) 159 E6 Weyl Group 27 cosets of (D5 = 2^4 x 5!) (27x16=9x6x8): 72 x 6! Automorphism group of 27 lines on cubic surface 160 72 E6 root vectors in 6-dim can project in 4-dim to 24-cell 161 E6 cohomology: 3 + 9 + 11 + 15 +17 + 23 E6 Casimirs: 2 + 5 + 6 + 8 + 9 + 12 = = 42 = 6 + 36 = 6 + 72/2 162 Spin(10) cohomology: 3 + 7 + 11 + 15 + 9 Spin(10) Casimirs: 2 + 4 + 6 + 8 + 5 = = 25 = 5 + 20 = 5 + 40/2 163 Spin(8) cohomology: 3 + 7 + 11 + 7 Spin(8) Casimirs: 2 + 4 + 6 + 4 = = 16 = 4 + 12 = 4 + 24/2 164 Witting Complex C4-Polytope: 240 vertices and cells 2160 edges and faces van Oss C2-3<4>3- 24 vertices 40 C3 hyperplanes-72 vertices 165 Witting Complex Honeycomb: 240 nearest neighbors van Oss apeirogon - 3<4>6 - - Eisenstein integers a + bw: w = (-1+iSqrt3)/2 166 F4-E6 Model: Weyl Group: Symmetric Anti-Symmetric Casimir Op. Lie Group Cohomology WickRotation Nilpotent BRS Contraction 167 Spin(10)/Spin(8)xU(1) = =rank4 quadric Q8 < CP9 < C10 Smooth quadric Q'4 = Klein quadric Q*4 < CP5 < C6 - - Twistor complex spacetime 168 Quadric Q8 < CP9 < C0: Q8 = C + iR8 = = Siegel right half plane C = light cone in R8 = = Silov Boundary RP1 x S7 169 Twistor Quadric Q*4 <CP5<C6 Q*4 = C + iR4 = = Siegel right half plane C = light cone in R4 = = Silov Boundary RP1 x S3 170 <0> => 0+Z+ => Z => Q => R R => C => H => O C-matrix M(m,n): Vm -> Vn Quiver of Arrows: <a-R->b> a-R->b <=> Vm -M(m,n)-> Vn 171 Simple Quivers: An Dn E6,E7,E8 An: /\(1)n ->/\(2)n ->...->(/\(n-1))n Dn: /\(1)2n ->...->(/\(n-2))2n <- <-(2^(n-1), 2^(n-1)) 172 78| 27 -> 351 -> 2925 -> 351 -> 27 E6 = D5 + D5(spinor) + C E7 = D6 + D6(spinor) + H E8 = D8 + D8(half-spinor) 173 28=8/\8 Gauge Bosons 8-d Spacetime 8+8 Fermions D4 D5 E6 Spin(8) Spin(10) E6 174 E6 -> F4 * | *--*--*--*--* *--*=<=*--* - J. McKay, P. Slodowy 175 D4 -> C3 -> G2 * | *--*--* *--*=<=* *=<--=* - J. McKay, P. Slodowy 176 D[n] -> C[n-1] * | * ... *--*--* * ... *--*=<=* - J. McKay, P. Slodowy 177 * ... *--* B[n] | A[2n-1] * -> * ... *=>=* | * ... *--* McKay, Slodowy 178 Sets =>A-D-E => D4-D5-E6-E7 states + states => QUANTUM => atoms ++ atoms => RNA, DNA => cells +++ cells => people ++++ people => civilization 179 + - Feynman Sums ++, +++, ++++ - Kauffman NK Boolean Network Sums K>4 => Chaos - Adaptation on Rugged Landscapes 180 Feynman Sums with Mass: Intermediate Interference (- compare R. Griffiths) Kauffman NK Boolean Sums: "Classical" Approximations 181 2^(n-1) Cl(2n) Half-Spinors are linear span of 1+(1/2)n(n-1) = 1 + Spin(n) Pure Spinors [isotropy group SU(n)] 182 78(E6) = 45(Spin(10)) + 32 + 1 32 = Spin(12) Half-Spinors 16 = Spin(12) Pure Spinors = = 1 + Spin(6) = 1 + SU(4) [isotropy group SU(6)] 183 16 = 8+8 Spin(8) Full Spinors 8 = Spin(8) Half-Spinors = 7 = Spin(8) Pure Spinors = = 1 + Spin(4) = 1 + S3 + S3 [isotropy group SU(4)=Spin(6)] 184 Birkeland Currents and Diocotron Instability => => Galactic Rotation Curve Flatness and Fine Structure - Peratt and Bostick 185 You shall know the truth, and the truth shall make you free. - Gospel of John 8:32 186 Polaris: vRCHO1 Arcturus: qCi Vega: s-O1 Altair: s+O1 Ladle: HO1,HOi,HOj,HOk,O1e,Oie,Oje,Oke Hsiu: 28 (4) I Ching: 8x8 = 64 Wei Chi: Qsum, (1+8+1+8+1)^2 187 Unless you make the right hand like the left; above like below; and behind like before: you will not see the kingdom. - Acts of Peter 38 188 Where the beginning is, there will the end be. - Gospel of Thomas 18 189 The universe was created by a fluctuation in the unbounded Apeiron causing separation into opposites. -- Anaximander 190 Constructible Set Theory is consistent if ZF is consistent. -- Godel (see Devlin) 191 In Constructible Set Theory, the Axiom of Choice and the Continuum Hypothesis are Decidable and True. -- Devlin 192 24-Cell: 24 8 12 6 2 96 3 3 3 3 96 2 6 12 8 24 193 Witting Polytope: 240 27 72 27 3 2160 8 8 8 8 2160 3 27 72 27 240 194 You can't always get what you want, BUT if you try, you just might get what you need -Glimmer Twins 195 Human minds, capable of premonitions, can leave the tyranny of matter to join OVERMIND. -Clarke (Childhood's End-'53) 196 OVERMIND network is alive, pulses with light, and communicates by colors and shapes. -Clarke (Childhood's End-'53) 197 OVERMIND has its limits. Material, individual, Overlords are its interpreters. -Clarke (Childhood's End-'53) 198 The opinions expressed in this book are not those of the author. -Clarke (Childhood's End-'53) 199 Parallelizable Manifolds: An Dn E6,E7,E8 Bn Cn G2 F4 - -Torsion=Structure Constants; S7-Torsion varies-Associator. - Cederwall and Preitschopf 200 Parallelizable Spheres: S1 = U(1)-C-Commutative-T=0; S3 = Sp(1)-H-NonCom-T=const; S7-O-NonAssociative-varying T - Cederwall and Preitschopf 201 Covariant Derivatives: Metric: D = d + G Parallelizing: ~D = d + ~G Torsion: T = ~D - D = ~G - G - Cederwall and Preitschopf 202 [ ~Da , ~Db ] = 2 Tabc(x) ~Dc Lie Group => Tabc(x) = Tabc(1) S7 => Tabc(x) - Tabc(1) = = Associator - Cederwall and Preitschopf 203 Octonion Alternativity => =>Aut(O) = G¤ = DerO ‰ d(a,b)x = = [a,b,x] + (1/3)[[a,b],x] So: S7 Associators <=> G2 - (see Sudbery) 204 S7 ~x Associator ~x Position = = O0 ~x Aut(O) ~x O0 = = S7 ~x G2 ~x S7 = = Spin(8) 205 Simple Catastrophe Germs: 1 variable: A2,A3,A4,A5,A6 2 variables: D4, D5, D6, E6 - Gilmore 206 Catastrophe Germs: D4 = A^2B + B^3 D5 = A^2B + B^4 E6 = A^3 + B^4 - Gilmore 207 E6 Catastrophe Perturbation: 1 A B AB B^2 AB^2 -Gilmore

208 E6 extended Coxeter-Dynkin: 1 2 3 2 1 2 1* - McKay, Sirag 209 E6 balance number squares: 1^2+2^2+3^2+2^2+1^2+2^2+1^2 = 24 24 = order of <2,3,3> = BT = = Binary Tetrahedral Group - McKay, Sirag 210 7x7 Character Matrix of BT: Columns are eigenvectors of 7x7 E6 extended Cartan Matrix 6 non-zero eigenvalues - McKay 211 McKay ADE Correspondence: D4 <-> BD2 = <2,2,2> (8) D5 <-> BD3 = <2,2,3> (12) E6 <-> BT = <2,3,3> (24) - McKay 212 E6 ext Cartan: BT Character-Egnval: 0 2 3 3 4 1 1 2 -1 0 0 0 0 0 1 1 1 1 1 1 1 -1 2 -1 0 0 0 0 2 0 -1 -1 -2 1 1 0 -1 2 -1 0 -1 0 3 -1 0 0 3 0 0 0 0 -1 2 -1 0 0 2 0 -w -w2 -2 w w2 0 0 0 -1 2 0 0 1 1 w w2 1 w w2 0 0 -1 0 0 2 -1 2 0 -w2 -w -2 w2 w 0 0 0 0 0 -1 2 1 1 w2 w 1 w2 w 213 D5 extended Cartan Matrix BD3 Character Matrix 2 0 -1 0 0 0 1 1 1 1 1 1 0 2 -1 0 0 0 -1 -1 1 1 1 1 -1 -1 2 -1 0 0 0 0 2 1 -1 -2 0 0 -1 2 -1 -1 0 0 2 -1 1 2 0 0 0 -1 2 0 -1 1 1 -1 1 -1 0 0 0 -1 0 2 1 -1 1 -1 1 -1 Eigenvalues -> 2 2 0 1 3 4 214 D4 extended Cartan Matrix BD2 Character Matrix 2 0 -1 0 0 1 1 1 1 1 0 2 -1 0 0 -1 -1 1 1 1 -1 -1 2 -1 -1 0 0 2 0 -2 0 0 -1 2 0 1 -1 1 -1 1 0 0 -1 0 2 -1 1 1 -1 1 Eigenvalues -> 2 2 0 2 4 215 A-D-E Classifications: Simple Quivers of Arrows Catastrophe Singularities Binary Polyhedral Groups Weyl Groups - Lie Algebras 216 Quantum Lattice - Group 24-cell - <2,3,3> Pure States: <±1,±i,±j,±k> Coherent: <(±1±i±j±k)/2> Phase: Complex Lattice 217 LIE ALGEBRA: Weyl Group W Finite Group on Weyl Chambers Spherical Reflection Rep. NO integer lattice translations I - Fulton and Harris 218 Affine Weyl Group: W x G0 (Hyperbolic Reflection Rep.) Euclidean Reflection Rep.: LIE GROUP G: Pi1(G) = I / G0 - Humphreys, Brown, Adams 219 Kleinian Singularity S = C2/G G = finite subgroup of SU(2,C) H2(S,Z) = C1 + ... + Cr Intersection Matrix of Ci = = - Cartan = A-2I -Slodowy 220 E6 - rank 6: 1,2,3,2,1,2,1 = = first Chern numbers (Sing.) 1+2+3+2+1+2+1=12: Coxeter 1+4+9+4+1+4+1=24: BT order E6<=>3.F24::E8<=>Monster -McKay 221 <±1> -> C2=(2,2,1) -McKay-> A1 |Weyl Spin(3)=SU(2)=Sp(1)=S3 -> A1 222 <±1,±i>->(2,2,2) ->[<2,2,2>->D4]/2 |Weyl |McKay| Spin(4)+SU(3)->G2 +S7+S7 -> D4 |Weyl <±1,±w,±w^2>->(2,2,3)<-M>->D5/2 223 <24-cell> -> BT -McKay-> E6 |Weyl D4 + D5/D4 + E6/D5 -> E6 17| |33 CxV8+S1 Cx(S8-+S8+)+S1 224 <24,24*> -> BO -McKay-> E7 |Weyl F4 + S3 + 3x26 -> E7 || D4+V8+S8-+S8+ 225 Witting = 2x(24 + (Golden 96 of 24*)) <Witting> -> 2xBI -MK-> 2xE8 |Weyl E8 2xD8 + (S16-+S16+) -> 2xE8 2x120 2x128 2x248 226 Quaternion Group <p,q,r> | | Weyl Group [3^(p-1),(q-1),(r-1)] - Coxeter (Ford and McKay) 227 Unit Integral Lattices: R - B1=A1=C1 Integers Z C - D2 Gaussian, A2 Eisenstein H - D4 24-cell, F4 (24 + 24*) O - E8 Witting = 2x(24 + (Golden 96 of 24*)) 228 Science is the most reliable guide in life. - Mustafa Kemal (Ataturk) 229 28 Spin(8) G0; G1; G2; G3; G4; G5; G6; G7 15 SU(4) G0 -iG1; G2 -iG3; G4 -iG5; G6 -iG7 10 Sp(2) G0 -iG1 -jG2 -kG3; G4 -iG5 -jG6 -kG7 7 S7 G0 -iG1 -jG2 -kG3 -eG4 -ieG5 -jeG6 -keG7 230 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

231 Spin(8) - Z2^3xS4 - 192 | Spin(5)&endash;SU(3)&endash;Spin(4)&endash;U(1)^4 Z2^2xS2 S3 Z2xS2 1 8 6 4 1 232 Spin(0,8): Cl(0,8) = R(16) Cle(0,8) = Cl(0,7) = = R(8) + R(8) R(8) = T = (CxQ) x O R(8) = Cl(0,6): Spin(0,6) 233 0 2 2 2 2 2 2 2 1 4 4 2 2 2 2 2 2 1 4 4 4 2 2 2 2 2 1 4 4 4 4 2 2 2 2 1 4 4 4 4 4 2 2 2 1 4 4 4 4 4 4 2 2 1 4 4 4 4 4 4 4 2 1 4 4 4 4 4 4 4 4 1 234 0 U U U U U U U 1 4 4 U U 2 U U U 1 4 4 4 U 2 2 U U 1 4 4 4 4 2 2 2 U 1 4 4 4 4 4 2 2 2 1 4 4 4 4 4 4 2 2 1 4 4 4 4 4 4 4 2 1 4 4 4 4 4 4 4 4 1 235

U U U U 1 U U U U 1 U U U U 1 U U U U 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 0 1

236 Spin(0,6): Cl(0,6) = R(8) Cle(0,6) = Cl(0,5) = C(4) Re(C(4)) = R(4) survives Im(C(4)) = R(4) collapses 237

4 4 4 4 4 4 4 4 Re(C(4)) 4 4 4 4 4 - U(4) 4 4 4 4______________________ 3 3 3 2 Im(C(4)) 3 3 3 2 3 - U(3) 3 3 3 2 2 - SU(2) 0 0 - Higgs

238 Im(C(4)): U(3) = U(1) x SU(3) SU(2) Higgs SU(2) Scalar 239 Re(C(4)):U(4)=Spin(0,6)xU(1) U(1)<->Dirac Complexification Spin(0,6) = Spin(0,5)xS5 Spin(0,5) <-> McDM E-H Gravity S5=Conformal -> NP Q Gravity 240 Cle(0,6)=Cl(0,5)=C(4)=Cl(2,3) Cle(0,5)=Cl(0,4)=Q(2)=Cl(1,3) CxQ(2) = C(4) = Dirac Cle(2,3)=Cl(2,2)=R(4)=Cl(3,1) CxR(4) = C(4) = Dirac

Thanks to Philip Dorrell for comments, for corrections with respect to the genetic code, and for reference to a Many-Worlds FAQ.

With respect to many of my web pages, thanks to Kent Davis for letting me know about some bad links and other errors, so that I could correct them.

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