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Wedges as displacement into the fourth dimension
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The conventions adopted for GDA are meant to accommodate greater
density of information display without use of italics, subscripts,
superscripts, multiple fonts, foreign language symbols, or graphics.
If half of the 52 symbols used for English might later be deemed
ambiguous in shape, there are still many more than ([26]^3) label
possibilities available for up to three symbols in brackets:
[Gye] = Gyromagnetic ratio of the electron, [4Pi] = Four times Pi,
[qD0] = Atomic unit of electric quadrupole moment, [p] = momentum,
[c^2] = Square of speed of light, etc.
If four letters are used to identify a unit, then with or without
parentheses, brackets, braces, or slash marks these rules can apply
AND be used in conjunction with established standards of expression:
1. A capitalized first letter means a positive exponent, if the
first letter is not capitalized then the unit has a negative power.
2. Numerals in the second and third positions of the four letter
unit label denote the numerator and denominator of the fractional
power to which the unit is raised, and lack of a numeral in either
internal position correlates to the presence of numeral one:
Ampere : Ampr Joule: Juul Newton : Nwtn Steradian: Strr
Coulomb: Cuul Katal: Katl Ohm : Ohmm Sievert : Svrt
Farad : Frad Lumen: Lmen Pascal : Pscl Tesla : Tsla
Gray : Gryy Lux : Luxx Radian : Radn Volt : Vltt
Henry : Hnry Meter: Metr Second : Scnd Watt : Waat
Hertz : Hrtz Mole : Mool Siemens: Smns Weber : Webr
Becquerel: Bcql Hrtz = scnd Scnd = hrtz Kilogram : Kgrm
degrees Centigrade: Degc Candela = Cnda degrees Kelvin: Degk
([Farad]^+1) = Frad = F1ad = F11d = Fr1d ; ([Farad]^-1) = frad
([Meter]^2) = M21r = M2tr = MetrMetr ; ([Meter]^-.5) = me2r = m12r
([Meter]^2) = [Volt][Second]/[Tesla] : M2tr=ScndtslaVltt
[Volt]=[Weber]/[Second] : Vltt=scndWebr=Webr/Scnd=1/Scndwebr
[Ampere]=[Weber]/[Henry] : Ampr=Webr/[Henry]=hnry[Weber]=hnryWebr
[Watt]=[Volt][Ampere] : [Watt]=[Ampere]/vltt=Vltt/ampr=AmprVltt
[Siemens]=[Coulomb]/[Weber] : Smns=Cuulwebr=[cuul^-1]/Webr
[Hertz]/[Tesla]=[Coulomb]/[Kilogram] : Hrtztsla=1/ScndTsla=Cuulkgrm
[Hertz] = 1/[Second] = [Siemens]/[Farad] : Hrtz=scnd=fradSmns
[Second] = [Ohm][Farad] : Scnd=FradOhmm : S2nd=F2adO2mm
[Second^2] = [Henry][Farad] : S2nd=FradHnry : Scnd=F12dH12y
[Henry] = [Ohm^2][Farad] : Hnry=FradO2mm : H12y=F12dOhmm
[Henry] = [Ohm][Second] = [Kilogram][Meter^2]/[Coulomb^2] :
Hnry=OhmmScnd=c2ulKgrmM2tr
[Farad] = [Coulomb^2][Second^2]/([Meter^2][Kilogram]) :
Frad=C2ulkgrmm2trS2nd : F12d=Cuulk12mmetrScnd
[Weber^2] = [Joule][Henry] = [Kilogram][Meter^2]/[Farad] :
W2br=HnryJuul=fradKgrmM2tr : Webr=H12yJ12l=f12dK12mMetr
[Coulomb^2]=[Joule][Farad] : C2ul=FradJuul : Cuul=F12dJ12l
[Kilogram]/[Henry] = [Coulomb^2]/[Meter^2] : hnryKgrm=C2ulm2tr
[Kilogram] = [Farad][Meter^2][Tesla^2] =FradM2trT2la
= [Coulomb^2][Henry]/[Meter^2] =C2ulHnrym2tr
= [Coulomb^2][Second^2]/([Meter^2][Farad]) =C2ulfradm2trS2nd
= [Ampere^2][Ohm][Second^3]/[Meter^2] =A2prOhmmm2trS3nd
= [Coulomb][Second][Tesla] =CuulScndTsla
:::::::::::::::::::::::::::::::::++:::::::::::::::::::::::::::::::::
An asterisk on the far right of an entry below denotes the presence
of a factor of rotation or geometry that may be improper to treat as
merely numerical on all scales in a curved universe.
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For a term of form: [MASS^x][LENGTH^y][TIME^z]{([Meter]/[Farad])^s}:
ENTRY has dimensions: x y z s
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AUN = Atomic unit of . . . .
[2Pi]=2 times [Pi] 0 0 0 0*
[2af]=[2Pi][f0] = AUN frequency scnd 0 0 -1 0*
[4Pi]=4 times [Pi] 0 0 0 0*
[18P]=AUN Electric Polarizability C2uljuulM2tr 0 3 0 -1
[19H]=AUN 1st Hyperpolarizability C3ulj2ulM3tr -1/2 3/2 1 -3/2
[20H]=AUN 2nd Hyperpolarizability C4ulj3ulM4tr -1 4 2 -2
[23M]=AUN magnetizability Juult2la 0 5 -2 -1
[29H]=[H0][[4Pi]{[aa]^2} Amprmetr 1/2 1/2 -2 -1/2*
[43P]=(4 times [Pi])/3 0 0 0 0*
[a ]= Acceleration Metrs2nd 0 1 -2 0
[a0]= AUN length = Bohr atom radius Metr 0 1 0 0
[A ]= Area M2tr 0 2 0 0
[A0]= AUN area = [4Pi]([a0]^2) M2tr 0 2 0 0*
[aa]= Fine structure constant 0 0 0 0
[aBH]=[FBH]/[PM] Metrs2nd 0 1 -2 0
[aD]= Absorbed dose Gryy=Juulkgrm 0 2 -2 0
[ae]= [Fe]/[Me] Metrs2nd 0 1 -2 0
[amu]=Atomic mass unit = [10^-26.7797510 Kgrm] 1 0 0 0
[An]= Avagadro constant molecules/[Mool] 0 0 0 0
[aR]= Absorbed dose rate Gryyscnd 0 2 -3 0
[b ]= Mass frequency Kgrmscnd 1 0 -1 0
[B ]= Magnetic flux density Tsla=m2trWebr 1/2 -3/2 0 1/2*
[B0]= AUN Magnetic flux density Tsla 1/2 -3/2 0 1/2*
[BHR]=[G]/[c^2] kgrmMetr -1 1 0 0
[Bk]= Boltzmann constant degkJuul 1 2 -2 0
[Bm]= Bohr Magneton AmprM2tr 1/2 7/2 -2 -1/2*
[c ]= Speed of light in vacuum Metrscnd 0 1 -1 0
[c^2]= [c] times [c] M2trs2nd 0 2 -2 0
[C ]= Capacitance Frad=Cuulvltt 0 1 0 -1
[Cm]= Compressibility = ([V]/[Pr])/[V] pscl -1 1 2 0
[Cn]= Conductance Smns=ohmm 0 1 -1 -1
[cQ]= Circulation quantum M2trscnd 0 2 -1 0*
[Ct]= Conductivity metrSmns 0 0 -1 -1
[Cw]= Compton wavelength Metr 0 1 0 0
[d ]= Magnetic constant, permeability Hnrymetr 0 -2 2 1*
[D ]= Mass density Kgrmm3tr 1 -3 0 0
[De]= Dose equivalent Svrt=Juulkgrm 0 2 -2 0
[Dp]= [Mp]/([4/3][Pi]{[Rp]^3}) Kgrmm3tr 1 -3 0 0
[DQ]= [Me]/([4/3][Pi]{[Re]^3}) Kgrmm3tr 1 -3 0 0
[e ]= Energy, work, heat Juul=MetrNwtn 1 2 -2 0
[E ]= Electric field strength metrVltt 1/2 -1/2 -1 1/2
[E0]= AUN electric field strength metrVltt 1/2 -1/2 -1 1/2
[eD]= Energy density Juulm3tr 1 -1 -2 0
[Ed]= Electric flux density Cuulm2tr 1/2 -1/2 -1 -1/2
[Ef]= Electric flux Cuul 1/2 3/2 -1 -1/2
[Eg]= Electric field gradient m2trVltt 1/2 -3/2 -1 1/2
[Eg0]=AUN electric field gradient m2trVltt 1/2 -3/2 -1 1/2
[Ep]= Electric polarization metrVltt 1/2 -1/2 -1 1/2
[eS]= Specific energy Juulkgrm 0 2 -2 0
[eV]= Electron-volt = [10^-18.7952897 Juul] 1 2 -2 0
[Ex]= Radiation exposure Cuulkgrm -1/2 3/2 -1 -1/2
[f ]= Frequency Hrtz=scnd 0 0 -1 0
[f0]= Bohr electron orbital frequency Hrtz 0 0 -1 0
[F ]= Force Nwtn 1 1 -2 0
[FBH]=[G]{[PM]^2}/{[PL]^2} = [c^4]/[G] Nwtn 1 1 -2 0
[Fe]= [Ke]([Q0]^2)/([a0]^2) Nwtn 1 1 -2 0
[Fg]= [G][Me][Mp]/([a0]^2) Nwtn 1 1 -2 0
[Fge]=[G]([Me]^2)/([a0]^2) Nwtn 1 1 -2 0
[Fgp]=[G]([Mp]^2)/([a0]^2) Nwtn 1 1 -2 0
[FPC]=[d]{[PC]^2} Nwtn 1 1 -2 0
[FPQ]=[Ke]{[PQ]^2}/{[PL]^2} Nwtn 1 1 -2 0
[FPX]=[Ke]{[PX]^2}/{[PL]^2} Nwtn 1 1 -2 0
[g ]= Earth acceleration of gravity kgrmNwtn 0 1 -2 0
[G ]= Gravitational constant k2rmM2trNwtn -1 3 -2 0
[G0]= Conductance quantum Smns=ohmm 0 1 -1 -1
[Gev]= [10^9 eV] = [10^-9.7952897 Juul] 1 2 -2 0
[Gy]= Gyromagnetic ratio AmprkgrmScnd -1/2 3/2 -1 -1/2*
[Gye]=Gyromagnetic ratio of electron Cuulkgrm -1/2 3/2 -1 -1/2*
[Gyn]=Gyromagnetic ratio of neutron Cuulkgrm -1/2 3/2 -1 -1/2*
[Gyp]=Gyromagnetic ratio of proton scndtsla -1/2 3/2 -1 -1/2*
[h ]= Planck constant JuulScnd 1 2 -1 0
[H ]= Magnetic field strength Amprmetr 1/2 1/2 -2 -1/2*
[H0]= AUN magnetic field strength Amprmetr 1/2 1/2 -2 -1/2*
[hB]= AUN action = [h]/[2Pi] JuulScnd 1 2 -1 0
[He]= AUN energy Juul 1 2 -2 0
[Hu]= Hubble constant Hrtz 0 0 -1 0
[i ]= Current Ampr=Cuulscnd 1/2 3/2 -2 -1/2
[i0]= AUN current Ampr 1/2 3/2 -2 -1/2
[I ]= Inductance Hnry=amprWebr 0 -1 2 1*
[Im]= Impulse KgrmMetrscnd 1 1 -1 0
[Ir]= Irradiance m2trWaat 1 0 -3 0
[j ]= Current density Amprm2tr 1/2 -1/2 -2 -1/2
[Jf]= Josephson constant Hrtzvltt=webr -1/2 -1/2 0 -1/2*
[k ]= Electric constant, permittivity Fradmetr 0 0 0 -1*
[Ke]= 1/(4[Pi][k]) fradMetr 0 0 0 1*
[Kev]= [10^3 eV] = [10^-15.7952897 Juul] 1 2 -2 0
[Kv]= Kinematic viscosity M2trscnd 0 2 -1 0
[L ]= Length Metr 0 1 0 0
[Lcn]=Loschmidt constant m3tr 0 -3 0 0
[m ]= Magnetization Amprmetr 1/2 1/2 -2 -1/2*
[M ]= Mass Kgrm 1 0 0 0
[Ma]= Mass of alpha particle Kgrm 1 0 0 0
[Md]= Mass of deuteron Kgrm 1 0 0 0
[Me]= AUN mass = Mass of electron Kgrm 1 0 0 0
[Mev]= [10^6 eV] = [10^-12.7952897 Juul] 1 2 -2 0
[Mh]= Mass of helion Kgrm 1 0 0 0
[mI]= Moment of inertia KgrmM2tr 1 2 0 0
[Mm]= Mass of muon Kgrm 1 0 0 0
[mma]=Electron magnetic moment anomaly 0 0 0 0
[Mn]= Mass of neutron Kgrm 1 0 0 0
[Mp]= Mass of proton Kgrm 1 0 0 0
[Mt]= Mass of tau particle Kgrm 1 0 0 0
[Mtt]=Mass of triton Kgrm 1 0 0 0
[N ]= Wave number metr 0 -1 0 0
[Nm]= Nuclear magneton Juultsla 1/2 7/2 -2 -1/2*
[O ]= Origin 0 0 0 0
[p ]= Momentum KgrmMetrscnd 1 1 -1 0
[p0]= AUN Momentum KgrmMetrscnd 1 1 -1 0
[PA]= [4Pi]([PL]^2) M2tr 0 2 0 0*
[PB]= {[PM]/([k]{[PL]^3})}^.5 Tsla 1/2 -3/2 0 1/2*
[PC]= Planck current Ampr 1/2 3/2 -2 -1/2
[PE]= Planck energy Juul 1 2 -2 0
[Pf]= Planck frequency scnd 0 0 -1 0
[phi]=Natural proportion constant 0 0 0 0
[Pi]= Circle circumference to diameter ratio 0 0 0 0*
[PK]= Planck temperature Degk 0 0 0 0
[PL]= Planck length Metr 0 1 0 0
[PM]= Planck mass Kgrm 1 0 0 0
[Pp]= Planck momentum KgrmMetrscnd 1 1 -1 0
[PPw]=Planck power Waat 1 2 -3 0
[PQ]= Planck charge = ([hB][c][k])^.5 Cuul 1/2 3/2 -1 -1/2
[Pr]= Pressure, stress Pscl=m2trNwtn 1 -1 -2 0
[PRL]=[2Pi][PL] Metr 0 1 0 0*
[PT]= Planck time Scnd 0 0 1 0
[Pu0]=[PC]{[PL]^2} =Planck mag moment AmprM2tr 1/2 7/2 -2 -1/2*
[PV]= ([4Pi]/3)([PL]^3) M3tr 0 3 0 0*
[Pw]= Power Waat=Juulscnd 1 2 -3 0
[Pw0]=AUN power Waat=Juulscnd 1 2 -3 0
[PX]= ([hB][c][4Pi][k])^.5 Cuul 1/2 3/2 -1 -1/2
[q ]= Electric dipole moment CuulMetr 1/2 5/2 -1 -1/2
[q0]= AUN electric dipole moment CuulMetr 1/2 5/2 -1 -1/2
[Q ]= Charge Cuul=AmprScnd 1/2 3/2 -1 -1/2
[Q0]= AUN charge = Electron charge Cuul 1/2 3/2 -1 -1/2
[qD]= Electric quadrapole moment CuulM2tr 1/2 7/2 -1 -1/2
[qD0]=AUN electric quadrapole moment CuulM2tr 1/2 7/2 -1 -1/2
[QD]= Charge density Cuulm3tr 1/2 -3/2 -1 -1/2
[QD0]=AUN charge density Cuulm3tr 1/2 -3/2 -1 -1/2
[Q/M]=Specfic Charge Cuulkgrm -1/2 3/2 -1 -1/2
[QeM]=[Q0]/[Me] Cuulkgrm -1/2 3/2 -1 -1/2
[r ]= Resistivity MetrOhmm 0 0 1 1
[R ]= Resistance Ohmm=amprVltt 0 -1 1 1
[Ra]= Radionuclide activity Bqrl=scnd 0 0 -1 0
[Rc]= Rydberg constant metr 0 -1 0 0
[Re]= Classical electron radius Metr 0 1 0 0
[Rgc]=Molar gas constant degkJuulmool 1 2 -2 0
[RK]= von Klitzing constant Ohmm 0 -1 1 1
[Rn]= Neutron Compton wavelength Metr 0 1 0 0
[Rp]= Proton Compton wavelength Metr 0 1 0 0
[S ]= Poynting vector m2trWaat 1 0 -3 0
[St]= Surface tension Juulm2tr 1 0 -2 0
[T ]= Time Scnd 0 0 1 0
[Tc]= Thompson cross section M2tr 0 2 0 0*
[Tev]= [10^12 eV] = [10^-18.7952897 Juul] 1 2 -2 0
[Tp]= Proton characteristic time Scnd 0 0 1 0
[Tr]= Torque MetrNwtn 1 2 -2 0*
[u ]= Magnetic dipole moment AmprM2tr 1/2 7/2 -2 -1/2*
[u0]= AUN magnetic dipole moment AmprM2tr 1/2 7/2 -2 -1/2*
[ud]= Deuteron magnetic moment AmprM2tr 1/2 7/2 -2 -1/2*
[ue]= Electron magnetic moment AmprM2tr 1/2 7/2 -2 -1/2*
[um]= Muon magnetic moment AmprM2tr 1/2 7/2 -2 -1/2*
[un]= Neutron magnetic moment AmprM2tr 1/2 7/2 -2 -1/2*
[up]= Proton magnetic moment AmprM2tr 1/2 7/2 -2 -1/2*
[v ]= Velocity Metrscnd 0 1 -1 0
[v0]= AUN velocity Metrscnd 0 1 -1 0
[V ]= Volume M3tr 0 3 0 0
[V0]= ([4Pi]/3)([a0]^3) M3tr 0 3 0 0*
[Vi]= Dynamic viscosity m2trNwtnScnd 1 -1 -1 0
[Vmi]=Ideal gas molar volume M3trmool 0 3 0 0*
[vT]= Voltage Vltt=Cuulfrad 1/2 1/2 -1 1/2
[vT0]=AUN voltage Vltt=amprWaat 1/2 1/2 -1 1/2
[V]/[M]=Specific volume kgrmM3tr -1 3 0 0*
[w ]= Magnetic flux Webr=ScndVltt 1/2 1/2 0 1/2*
[w0]= Magnetic flux quantum Webr 1/2 1/2 0 1/2*
[Y ]= Angular momentum KgrmM2trscnd 1 2 -1 0*
[z ]= Impedance Ohmm 0 -1 1 1
[z0]= Intrinsic impedance of vacuum Ohmm 0 -1 1 1
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Numerical value as a power of ten for:
[2] + 0.3010300 [d ] - 5.9007901 [Lcn]+25.4292317 [PV]-103.7506794
[3] + 0.4771213 [E0] +11.7111495 [Ma] -26.1775275 [Pw0]- 0.7441541
[4] + 0.6020600 [Eg0]+21.9875484 [Md] -26.4757878 [PX] -17.7268723
[Pi] + 0.4971499 [f0] +15.8182050 [Me] -30.0405111 [q0] -29.0716885
[2Pi]+ 0.7981799 [FBH]+44.0817422 [Mh] -26.3004734 [Q0] -18.7952896
[4Pi]+ 1.0992099 [Fe] - 7.0841401 [Mm] -27.7250271 [qD0]-39.3480874
[18P]-40.7828380 [Fg] -46.4387750 [mma]- 2.9356722 [QD0]+12.0339070
[19P]-52.4939875 [Fge]-49.7026838 [Mn] -26.7760040 [QeM]+11.2452215
[20H]-64.2051370 [Fgp]-43.1748662 [Mp] -26.7766023 [Rc] + 7.0403543
[23M]-28.1028659 [FPC]+44.0817422 [Mt] -26.4992464 [Re] -14.5500682
[29H]+ 8.0974941 [FPQ]+42.9825322 [Mtt]-26.3003915 [Rgc]+ 0.9198347
[2af]+16.6163849 [FPX]+44.0817422 [Nm] -26.2966413 [RK] + 4.4118352
[a0] -10.2763989 [G ] -10.1744595 [p0] -23.7005250 [Rn] -14.8795607
[A0] -19.4535879 [G0] - 4.1108052 [PA] -68.4826355 [Rp] -14.8789625
[aa] - 2.1368347 [Gye]+11.2457248 [PB] +53.8813988 [Tc] -28.1770178
[aBH]+51.7445641 [Gyn]+ 8.2630373 [PC] +24.9912662 [Tp] -23.3557831
[ae] +22.9563709 [Gyp]+ 8.4273598 [PE] + 9.2908195 [u0] -22.7317025
[An] +23.7797510 [h ] -33.1787440 [Pf] +43.2677434 [ue] -23.0322291
[B0] + 5.3711635 [H0] +11.2719536 [phi]+ 0.2089876 [um] -25.3477103
[BHR]-27.1281008 [hB] -33.9769239 [PK] +32.1513055 [un] -26.0149166
[Bk] -22.8599163 [He] -17.3605390 [PL] -34.7909227 [up] -25.8505941
[Bm] -23.0327325 [Hu] -17.6028630 [PM] - 7.6628219 [v0] + 6.3399860
[c ] + 8.4768207 [i0] - 2.1789047 [Pp] + 0.8139988 [V0] -30.2071080
[c^2]+16.9536414 [Jf] +14.6844844 [PPw]+52.5585629 [vT0]+ 1.4347506
[cQ] - 3.4392630 [k ] -11.0528513 [PQ] -18.2764773 [w0] -14.6844844
[Cw] -11.6150537 [Ke] + 9.9536414 [Pu0]-44.5905793 [z0] + 2.5760306
[Me]/[Mp] = [Nm]/[Bm] = [Rp]/{[a0][2Pi][aa]} -3.2639088
[PX][PF] -25.5408711 [4Pi][aa] -1.0376248 [4Pi]{[aa]^2} -3.1744595
?
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