arithmetics and nomenclature

GLOSSARY, ACRONYMS ('anchronyms', in submariner jargon):

Mathematical nomenclature: (as it withstands improvement to clarify its utility in high-technology)

• At-sign, @ (or sometimes lowercase e), for a number "at" a place, position, so-many-tens, powers of ten, characteristic, scale, range, radix-ten exponent; scientific notation [rather than computer-traditional E, double-precision D]
  • e.g. 5.12@3 = 5120
  • e.g. 5.12@-3 = 0.00512
• Complex angle, & = ¢ + i$ "ensine equals cosine plus i (times) sine, of"
  • outer product, ⋅ , · , (angle summation) [dot/middot]
  • inner product, ⨪ , ∸ , ∸ , (angle difference) [dot minus/bar]
  • inner division, ÷ , (angle difference) [colon minus/bar]
  • outer division, : , (angle summation) [colon]
• Complexor, a complex-number-comprised-of-complex-numbers; quaternions, octonions; the mathematicians' 1,i,j,k notation for quaternions is a real+vector order appending to the concept of real number, 1, imaginary vectors, i,j,ij=k, extended to reach the complex and complexor numbers; space-time physicists entitle alphabetic-order, i,j,k,l (lowercase 1), appending 1D-time to 3D-space; Octonions append L,I,J,K, or, I,J,K,L (capitalized 1,l)
• Derivatives named, the (much-used) space-time moments:
  • The First Derivative of [scalar] distance, with respect to time is, speed, e.g. ft/sec
    The First Derivative of [vector] position, with respect to time is, velocity
  • The First Derivative of speed or velocity, with respect to time is, acceleration, e.g. ft/sec²
  • The First Derivative of [scalar] acceleration, with respect to time is, pump (not jerk *), e.g. ft/sec³
    The First Derivative of [vector] acceleration, with respect to time is, swing (not jerk *)
  • The First Derivative of pump or swing, with respect to time is, jerk (* not snap), e.g. ft/sec⁴
  • The First Derivative of jerk, with respect to time is, snap, e.g. ft/sec⁵ (order-higher-than 'jerk' *)
  • * (There is no jerk in smoothly changing the acceleration-aka-force vector, without sharply changing rate, focus, radius; cf circular-swing acceleration in spacetime-physics is deemed indistinguishable from artificial-gravity; cf pumping, swinging, bouncing, springing, tipping, change acceleration smoothly continuously; cf a hanging swing is pumped not jerked, to increase its profile derivatives, acceleration, speed, height, while swinging, itself, is felt and adapted-to, unnoticed aside gimbaled amusements; cf pumping brakes is equalizable by pumping back, not by 'excess' jerking except a cushion softens it, or by leaning back partaking more of the force of gravity, but, leaning is not instantaneous, ergo cannot be jerk... Jerk is a quickened derivative of pump by discontinuous/directional 'play'... cf 'mad' rollercoasters turn by strictly-circular arcs changing sideways acceleration instantaneously 'jerking' by radial-focus-discontinuity... Jerk is or-results-in abrupt-change of position, cf the Olympic Jerk is the abbreviated-pump emphasizing its derivative because slow-pumping wastes bioenergy... Cf similar technical terms such as 'squeeze-don't-jerk-the-trigger' meaning gradually increasing acceleration-like-pressure-force 'til its-own trigger-event... but also consider 'play and wobble' before 'jerk')
  • n.b. Jolt, is generally equated to jerk, though suggestive of harder and higher order
  • n.b. Jounce, is a jolt-bounce returning to its original-projected position and velocity
  • n.b. Throw, may be any of the five, scalar or vector
  • n.b. Heave, implies, massive, cf broadly-obviously mountain heavens, cosmic heavens
• Exponent placement-compounding symbolically increases involvement by deeper-application: (left) afore, upon, above, over, behind (right): where the deeper are more involved functionally-internally/argumentive-to rather than externally-usage-of:
• Exponent, of a term, placed upon, upper-fore of its root term [rather than as formerly over], as exponentiation is conceptually the iteration-extension above multiplication,- even as multiplication is the iteration-extension of addition
  • e.g. ²3 = 9 'square of 3'
  • e.g. ³2 = 8 'cube of 2'
  • e.g. ⁴3 = 81 'fourth power of 3'
  • e.g. ^-13 = 1/3 'inverse or negative power of 3'
  • e.g. ^-1sin = 1/sin
  • e.g. ²f x = ²(f x) = (f x)·(f x) = (f·f) x = (²f) x
  • e.g. ²log x = ²(log x)
• Exponent placement over, upper-aft its root operation, is the functional composition repetition-iteration notation (consistent with the traditional arc-function, inverse function, operator algebras)
  • e.g. sin^-1 = arcsin (already common usage)
  • e.g. f² x = (f f) x = f f x = f(f x)
  • e.g. log² x = log log x = llog x
  • e.g. f^-1(f x) = f^-1 f x = (f^-1 f) x = (1_f) x = x (in the domain of f; where f is 1-1)
  • n.b. x² = (x x) = x x = x(x) = x·x = ²x : Strictly nonfunction numeric variables and constants are the same either way
• Functions may have multiple, parameter-arguments, if so defined,--
  • e.g. f x y = f(x,y), is a two-argument function; generally ≠ (f x) y , unless—
  • n.b. (f x) y = f_x y , is a progressive-parameterization-application function, taking y as a subsequent separable, argument
• Gut arithmetic [aka matrix arithmetic but little new comes of vector sums of products: whence a gut process]
• Identity Operator, 1_i=j = 1 for i=j else = 0 for i≠j (assumed multiplicative null, empty, undefined); [cf δ_ij]
  • cf Logic Operator, (i=j) = true for i=j else = false for i≠j
  • e.g. Identity Matrix, [1_i=j] = [₀¹⋱₁⁰]
• Infinitesmal, ∂ "par, partial", a standalone numeric value-holder
• Derivative, δ "slope-of-, del-, deal-of-"; δ_xy = (∂/∂x) y "... over x, or with respect to x, of y"
  n.b. ∂_i = ∂ξ_i , generalizes dimensionality, e.g. ∇ = i(δ_i) + j(δ_j) + ... [rather than prior assumed scalar:vector, x:i, y:j,...]
• Integration interval, ∫_[x,y] closed, ∫_(x,y) open; or, ∫_[x+,y-] open, ∫_x<ξ<y∂ξ open, etc.
• Logarithm, £ x = ln x = log_e x 'natural log; ponent'
  cf The entropy of p , 0 < p < 1, is -p £ p (in natural base; binary base is more usual)
• Left-Multiplication is a property of addition, not an operation (no more so than parentheses or exponentiation). Addition may be any additive process: Multiplication is the iterative extension property thereof;- which is to say, a process is multiplicative only if it includes natural-number multiplication, e.g. matrix A*B , is multiplication only if, n*B already is and = n_i=j*B = [₀ⁿ⋱_n⁰]*B

  Multiplication always includes specifically intrinsic Left Multiplication, which has special necessary properties and is specifically denoted; Other-multiplicative process is distinguished as a, "product", if it does not include the intrinsic: To say, * , is the multiplicative operator on a ring, means, * , includes n*x : {n} = N₊ in the ring set;- And whence, y*x , imputes, y , may be any natural number: and therefor the ring set includes the set of all natural numbers (The ring set need not entirely separate them: cf modulo).... Thus, another-multiplicative process, X, existing on a ring, If , X , does not include intrinsic multiplication, makes for two actual operations, and three operation symbols, +,*,X , on that ring.

• Natural distribution, e^{-π x²/s²}/s , semidiameter s , var. s²/2π , identified by its 'knee/ankle' angular joints and inflections
• Arithmetic precedence: 'over' is positional formatting, 'divide' is arithmetic operation
• x/y+z "x over y plus z" is global = x/(y+z) ; cf x÷y+z "x divided by y plus z" is local
• a/bc "a over b c" adjacency precedence = a/(bc) = a/b(c) =
• a/b(c) functionlike precedence = a/(b(c)) e.g. a/2c = a/(2c) = a/2(c) = a/(2(c))
• Set notation specification, e.g. {i}, is simpler, or, more inclusive:
  • e.g. {i≤5} or {i:≤5} is the "set of i [that are] less than or equal 5"
  • e.g. {i: i; i(+,-); i≤5} is the "set of i where i exists, i is closed on addition and subtraction, i is less than or equal 5"
  • Note that i(+,-) is like the computer-logic denotation-as-needed of numeric value or logical "is-defined" value
• Teams of Operators [formerly groups of elements, but compounded elements are non-elemental; cf nuclear fusion is not addition creating new elements; cf sets have non operational elementals]
• Vector correlation, * , the sum of corresponding products; [formerly "dot product"]; the complex conjugate self-product (a)(a')
• Virtual, the imaginary dimensions of the octonion beyond quaternion; L,I,J,K or I,J,K,L
  • Virtual, generally means the venue of 8-complexors
  • Generally, the virtual, is the non real portion, including the imaginary
  • Specifically, the virtual, is that we've appended to the real and imaginary
  • 'Specifically virtual', requires three or more vectors more-complex-than, or non,-quaternion
• (We're converting from "half-life" 1/2-remains to "natural-life" 1/e-remains, as equals its average for inverse-exponential)
• We do arithmetic-checking-by-9's-and-11's ... There is no radix-2-arithmetic-checking-by-1's: we check-by-3's (binary-11's)
• We use now-standard-html special symbol-letters, √, ≈, ≤, ≠, ≡, →, ⇒, ⇔, ∂, δ, γ μ, π, Δ, Π, Σ, ∫, ∞, ∀, ∃, ∪, ∩, ⊂, ⊆, ∈, etc.
• (We use should-be-standard-and-or-better-implemented special-symbols, e.g. r˙, r¨)

• Units have long been shy of meaning, For example, Torque and Work are both in units of force×distance but Torque is perpendicular distance and static expressing a cross-product, while Work is parallel and moving expressing a dot-product... 'perpendicularity' and 'parallelity' and as well multiplication and division thereof are as necessary as Length and Angle... And for second example, Radian measure (Metric), is deemed a 'unitless' angle, arc length/radius, but is in-fact 2π^R/circle...
• In some articles, especially the extras, sci-fi screenplays, we use Metric Time, hesit, demur

• Aether, cosmic aether, we discuss as a real (coeternal) infinite-time-integrated infinite-space-defining infinitely-dense manifestation (tbd) of mathematical complexor development, not frame-relativistic "measure-space-time"; "open cosmos"
• Atomic power, commonly misnomered, refers to energy stored in electron orbitals below electrochemical and electroplasma "degenerate electrochemistry" trans-ficial orbitals, e.g. a H-1s electron boosted 6.3 eV to 2s , where maintained by rf-laser coupling the groundstate electron-spin potentials, it holds 69K°K till released; We discuss transition to p-e-p nuclear fusion
• Mass-hole (better-phrase), is a gravitational singularity, mass compressed beneath its nucleon (and quark) roche-threshold, to wave-entropical radius (tbd); a "black hole" not necessarily black; We discuss aether-noodle-fragmentation renormalization
• Nuclear, refers to atomic nuclear; energy, states, structure, bonds, chemistry, fission, fusion, inner bound electrons, protons, neutrons, deuterons, helons (alphas), ...; We discuss doubly-charged protons p⁺⁺ and negatively-charged neutrons n^-
• PE state, atomic-electron suborbital proton-electron state, cold-degeneracy to absolute-cold; an intension of the atomic model
• Relativity, is with-respect-to-the-speed-of-light 'limit', but we also discuss the correction-and-disproof of commonly mistaken notions, 'equivalence-principle'
• Subatomic, refers to β-exchange between a nucleus and a low-state or groundstate electron orbital, as in the Ho-Dy-163 co-version experiment; electrons, protons, neutrons, and related nuclear-size particles, nuclear fragments; We discuss antihelon stability "sitting" outside the closed 1s-orbital shell; see also Supranuclear
• Subnuclear, refers to nucleons, energy, interchanges; We discuss aether wavicles, "neutrino chop"
• Supraneutronium, (ferroneutronium is the most stable), refers to sub-absolute-zero-cold maximum atomic-density mass, cold-electron-degeneracy, not neutron star density but stable nuclear tendencies; not-yet-known to occur naturally but expectably
• Supranuclear, refers to electrons "sitting" just outside the nucleus, adsorption below groundstate without absorption-fusion
• TEMPEST, (military) acronym for various spurious-electronic-signal-emission suppression technologies, techniques, contractual requirements and standards, for operation under occasional (thermo)nuclear-detonation duress, developed in the 1950's-70's;
  Some common interpretations:
  • Thermonuclear Electro-Magnetic-Pulse Exception Suppression Technologies, meaning it didn't quit under nuclear assault ... cf reinforced concrete radio horns, fluted ferrite beads (nonsaturating) and spark gaps hung on every electric path, wire, sewer line ... above and beyond good electrical grounding and shielding techniques every engineer must use...
  • Thermo-Electronic-Magnetic-Pulse Emanation-Suppression Technologies, meaning EMP is not an electromagnetic radiowave but a ripping-hot electron-cascade avalanche pulse (zone-ionization) borne in an expanding magnetic field that couples and suppresses photonic emanation energy-loss,- thus keeping the pulse hot... (and affects chemistry)
  • Crypto-TEMPEST, was Transient Electro-Magnetic-Pulse Emission-Suppression Techniques, "Single-Point-Failure-Safe" electronic-ware design, preventing misdirection of messages in and after an EMP event not destroying a Crypto device...
  • TEMPEST Crypto, we do not discuss here, refers to Crypto [secret] messages during or pertaining-to nuclear warfare...
• Tuple, (mathematics) terminology: a doublet, a 2-vector, e.g. a complex number; a single-element consisting of a pair of terms ... Note that we use the term consistently: N-tuples here are N-pair elements [formerly N-part elements we here call, "N-uples"]
• -Uple, (mathematics) suffix to a [natural whole] number, meaning the part-count consistency of-or-defining an objectified unit

Grand-Admiral Petry
'Majestic Service in a Solar System'
Nuclear Emergency Management