MATHOUGHTS NOTES

('occasionally resorted-and-reorganized but probably-not this time')
_____

vector correlation dot product *

gut (matrix) arithmetic
  • semalog notation
  • significant figures
  • +6.0221387±20@23 ≡ +@23:60221387:20
  • sensitivity analysis: energy
  • fractional norm: entropic domain(size)
  • $ sine, cosine, osine, ensine
  • '?' conditional,'!' do-it, emphasis: ? x=y ! a=b
  • '/' over large-range: a+b/c+d ≡ (a+b)/(c+d)
  • '\' under large-range a+b\c+d ≡ (c+d)/(a+b)
  • inner difference product, outer difference product
  • '{}' set choices, '()' list event, '<>' phrase expression, '[]' vector complexor, eg: {!x=}
  • 30% 15% probability decidability
  • How close-or-far are, 100% more, and, 50% less---near the geometric mean, 29.29% across? Estimated as the halfway, 1/1.5 (33% away). _____
  • edit keys: SEARCH forward, SKIP back, CUT back, DEPOSIT forward, REPEAT, RECALL _____ ABM treaty vrs. place of fortification: Because the USA declined to implement one place of fortification under the ABM Treaty, Lanthus shall accession it, under the treaty, to the location of the GNSC outfitting facility. _____ units signature LFFT local vrs. GFFT global - i.e. wavelets calculatory statistics: 5-way numbers: Each number has its mean value; A �1% threshhold; A �1PPM threshold; For normal distribution the tail is very dense near the take-point. [10% above x1.09; 1% above x1.18; 0.1% above x1.26] extend to variable threshhold Let a: a,a+x,a+z be 50%,1%,1PPM - [alt 50%,0.5%,0.5PPM] a1+a2 = [a1+a2],[]+ [], []+x, []+x1+x2 []+x1+z2 ... _____ computation programming: memory regional multibit-parity, to catch unrelated code access; Functions should be as they naturally are: structured outputs of all computed results, not merely scalars and vectors, but out-parameter blocks: Parameters-in-parameters-out; matched and used as needed and present ... not merely at the microcode level but at the high-level language levels; cf (quotient, remainder) = integerdivision (dividend, divisor) , same-type units. cf (radius, angle) = polarcartesian (x-coordinate, y-coordinate) , different-type units. eg. x = integerdivision (m, n) ; xmodulus, xquotient, xremainder, meaning the same generic x-result instance as restricted or constrained to these three of multi-dimensional function value, as-if the function mapped onto its abscissa dimensions had differing range-types as well as range-values. or, modulusx, quotientx, remainderx, meaning these three values on-or-restricted-to the same x-result instance. eg. x = integerdivision(m, n); x.modulus, x.quotient, x.remainder, properties from the same instance. eg. document.selection.createRange().duplicate.moveEnd('character').select().focus(). ... where the outputs of moveEnd, select, focus, include-grab-chain the range-portion, and all the results are included in the final: the moveEnd scalar-distance, any yes-no, ... These are in some-essence, "non-forgetful, unforgetful, forgetless, elevant" functors: They include "latent, genetic, memory" of how they got calculated. 1. the instruction-address register needn't be additive-incremental -as requires fast-carry-lookahead,- but just uniquely-sequential,-- as by binary-polynomial-moduloing: Binary-polynomial-moduloing is bidirectional: irreducible polynomials have their obvious complement, using the same bit-taps except the end-taps are in-out-process-exchanged. (Irreducible polynomials usually need only a few bit-taps.) Bidirectional-sequential might implement: a. program code memory, which is unidirectional with jumps; b. stacks and queues which are two-ended bidirectional; c. text-strings. Polynomial-modulo-sequential is inherently random-memory. Program-memory can be subsequential-subpaged efficiently. 1.b. More energy-efficiently the address sequence can be grayscale 'one-address-bit-change-per' 2. program memory needn't decode alternate addresses so much as be in two halves: each decision chooses which-half. However classic subroutining needs specific large-address-switching,-- first-step and return-step not parallel-sequential in both halves. 3. Polynomial-modulo-sequential can directly-compute step-doubling, a tap-set per bit, as is useable for P^K-mod-Q encryption. _____ faster algorithms: 1. Compressed Multiplication-- 1.1. Complementation (subtraction) reduces the number of bit-multiplies by half; 1.2. Selective Complementation maybe further, e.g. 7 (3 bits) = 8 - 1 (2 bits); 1.3. Arithmetic Pattern compression: By finding repeated substrings in the multiplier, or multiplicand, the summation process can involve fewer terms, e.g. 1010001 contains 1001 twice: 1001000 + 0001001 which differ only by fast-shift; 1.4. Similarly Bit Pattern compression; e.g. where x,y are high-bit-density numbers, x¯,y¯ are low-density and so are -x,-y = x¯+1,y¯+1 1.5. fast-first-partial-representation of digital numbers maintained until just one, last, final, fast-lookahead-carry-stage renormalization for saving results 1.6. cf multiplication by 3-adders 1.5-bits/stage vs. carry-lookahead full-adders 1.41 bits/stage _____ HDTV: (near-future digital HDTV... signal-compatibility... noncompatible codes) The NTSC original used a suppressed carrier, vestigial side-band, almost as energy-efficient as single-side-band SSB discuss slow-scan on digital HDDV to move 0.5 pixel-grain/refresh = 15/sec digital treble-thread-gemming HDDV projector gaussian is not exact for quantized numbers on line. Just very close (and fast close). analysis of, address scattering in program memory _____ computation: pointspace interpolation, local point-nets, insertion/coalescence/extraction of points, primitive non-tidal point-domains, advanced dual-point tidal domain computation: (new age Internet) blessed distribution Prograham's seed, authenticatable program [source] encouraged registration/profits/distribution exponential distribution: unique net nodes; expectable entropic tap key generation-advance - copy from source: workable - blessing: speed-up 3x - publicly verify signature (authenticity) - consumate: owner name, pass key, offering (temple coffer) coded blessing - new code - new key, owner, pass key - renewal offering/blessing - interleave code - direct name - cpu exercise - arithmetic verification checking - code-scan/check - store compression - slow monitor calls - multi-key - network crosscheck - advertisements - code block-coding - vendor back-pointer - floating vrs. integer optimizations - piecewise code branching - interpreter vrs. compiled - random stack (dynamic allocation) - require skill exercise midstream - random code check - modem - the promised glory _____ checkwriter: _____ nomenclature terminology: deflection standard - deviation standard _____ education problem set generation: - maximum distribution research: {NASA} data - high schools, colleges _____ mathematics instructor: - question set generator - encyclopedia - grade - base tutoring - referencing - idea composition: hierarchy + cross-referenced - view magnification - reference path selection criteria/keying-actuation _____ document similarity 'plagiarism' detection statistical rules (Cf word proximity) _____ 6-segment/bar numerals (based on written-8: 4-elbow, 7-top, 1-top, 1-bot, 2-bot, 3-knee) _____ wavicle structures and interactions: optical interferometry - re-lasered photons in the stellar atmosphere, photosphere neutrinos as half-width photons, neutrino absorption spectrum
  • as protons (nuclei) have smaller than electron-sized shells:
  • a gravity singularity might also have a shell, one electron radius:
  • this results in the entire star becoming like 10^20 stars
  • a cosmos in renormalized micro-mass: -- dimples around an upwelling in a calm pool of water
  • cosmos initial event (condensation and renormalization) may result in aether ringing, giving it quantum-ization
  • or relatedly, the mass-regularity of individual neutrons (and very-likewise protons) in the holing event, gives the hole-aether a spatial ringing frequency,- and quantum-ization
  • and likewise the proton+neutron nucleation event in the instantly-subsequent Big Bang, gives the new-aether a temporal+spatial ringing frequency spectral enhancement spike, over mere thermal-spectrum
  • also possibly at Big Bang energy-densities, if quarks form in the instant-before, then the particle-count-drop by factor-of-3 bumps the temperature by a factor-of-3 a photon is about a half-wave long UHF neutrino, radio _____ other methods for propulsion: electric acceleration in the solar system on the sun's thermionic charge _____ digital treble-thread-gemming, HDDV projector improve to HDTV now (television.html original concept) _____
  • compound scalars
  • precise number measurement
  • half-point integration
  • infinitesimal
  • number density, countability
  • computus - matriculus - calculus - consumus
  • representational arithmetic - radix grafted
  • unit-scale signature-check
  • anathematics - FORTRAN 92
  • notation 2+2 = 2×2 = 22 = 22 = 2 2 _____ calculus: (something that always bothered thought since pre-freshman college) We differentiate ('take the derivative') and drop doubly-infinitesimal terms ('∂x2'); But if we double-integrate that ('∫∫∂x2'), shouldn't we have wiser kept, those terms, cf when we find antiderivatives we add 'C' which cancels in the evaluation (∫ab0=C-C=0), So, just-maybe those dropped-terms should be looked-at again, for 'information'... _____ 'Maxwellian' E&M equations: (electromagnetism, quantum mechanics, gravity) Where, is the term for gravity-- If we have a solar-mass of photons traveling across the universe, It must have a solar-mass of gravity (light is bent by gravity ergo pulls sideways), Yet as photons escape (diverge-from) that solar-mass, they lose energy, But to what--? The remaining photons have no rest-mass to increase potential...! And space-itself is not-yet attributed with tenuous-mass-energy...(except ΛCDM)... So, photons need a gravity term, slow-down and blueshift as they approach each-other... (Maybe it has to do with overlapping sinewaves being taller ergo slower-via...) (Note also that photons are, notably, electromagnetically 'couple'able...) _____ successor functions: ('beware of informalities') It seems that some authors are negligent of formalities, and switch tracks: e.g. 0 ≝ {} 1 ≝ {0} 2 ≝ {1,0} -but should be, to be consistent- 0 ≝ {} 1 ≝ {0,} 2 ≝ {1,0,} And there may be others who use a simpler computorial successor e.g. 2 ≝ {1} ≝ {{0}}, etc. _____ listing vs. finding in infinite sets: If we have a list of all rationals on the interval (0,1) typically denoted {m/n : m<n, ∈N}, and toss a number, an irrational, into the middle of that interval-list, it'll never be found: There are infinitely many elements in-between before-and-aft, though the total-infinity is the same... _____ infinitesmal, infinitesimal, infinite-small: ('20 min. beyond high school') is represented numerically as 0+, 0−, ∂, and differentially (taking a derivative) as dx, ∂x, and 1/0+ = +∞, 1/0− = −∞, and conversely 1/+∞ = 0+, 1/−∞ = 0−, but 1/0 is undefined (cf +∞ ≠ −∞) and so, in the geometry postulate of unique parallel lines in flat space, there is a line tilted 0+ and a line tilted 0− on opposite sides of the unique parallel line except, crossing through the defining point, and, they 'intercept, one at positive-infinity, the other at negative-infinity', (the undefined 1/0 case may be handled as an analytic continuation in complex number theory)... _____ implicit definitions: ('an interesting instance of proof') an irrational arithmetic sequence, an n∈N≥0, is closed at the n=0 end but open at the n→∞ 'end'; but then if wrapped around a unit circle it implicitly-defines its opposite arithmetic sequence, (⌈a⌉-a)n , and, welded together at a0 = (⌈a⌉-a)0 the compound-definition is thus both 'ends' open, (stepwise 'continuous' at n=0 but its stepwise 'derivative' has a discontinuity there)... _____ removing a point or points from a line or boundary: 1. cannot be done arithmetically as there are ~infinite many~ points adjacent at zero-distance; 2. so, logically, removing the point, is the usual method used in high school set theory, but 3. logic requires fancy arithmetic of removing an infinitesimal interval, around that point... _____ deep space net:
  • vid-link communication
  • information
  • computation service
  • remote telemetry - DeepSpaceNet extension - delay-line
  • government surplus
  • government role needs _____ font: Q's-complement Formal halfspace (especially in monospace, Typewriter, etc.) _____ keyboard: (26+2key) 0=O, 1=I/L, 2=Z, 3=E, 4=N/H/Y, 5=S, 6=G 7=T/F, 8=B/$, 9=P/Q the English-to-Greek-symbol letter mapping is odd in places, and might be done better:

    (Eng.) A a B b C c D d E e F f G g H h I i J j K k L l M m N n O o P p Q q R r S s T t U u V v W w X x Y y Z z
    (Grk.) A a B b C c D d E e F f G g H h I i J j K k L l M m N n O o P p Q q R r S s T t U u V v W w X x Y y Z z
    (Sug.) A a B b J s D d E e F f X x H h I i Q q K k L l M m N n O o P p Y y R r S V T t U u v j W w C c G g Z z
    (cf the French alphabet names "Y y" as "ee-grec") _____ display: numeric: pos-neg representation for easier readability for changing numbers-- 1. for numbers counting up, when counting back down go locally-negative; 2. for numbers counting down, when counting back up go locally-positive: e.g. ...28,29,30,31,30,31,30,31,30,31,32...39,20,21,22,21,20... --so that the more-significant digits appear, unchanged-- whence more readable. _____ music: An interest since high school: to mathmematically construct a model of Beethoven's Eighth (piano), particularly the introductory sequence, as a sample of music-speak, formatting: Eg. the first chord: 3-low-C Eb G C low-C Eb G C: the piano fills-in several harmonics for each note, and we may consider the complete fill as the intended:-- even the full spectrum ... thus the chord progression would include not rise so much as spread. The notes themselves on the tempered scale are nominally 1-3-7-12, plus the next octave: 1.000, 1.189, 1.498, 2.000, plus 4.000, 4.757, 5.993, 8.000 ... and the harmonic fill (interpolative). But the tempered scale can also cloak the intended notes-- possibly: 1.000, 1.200, 1.500, 2.000, --much simpler, but within 1.000, 1.009, 1.001, 1.000-- and the principle beats, .200 (5x,6x), .300 (4x,5x), .500 (2x,3x,4x), .800 (3/2x, 5/4x), and 1.000 (1x,2x) near-transparent octaving; and likewise their harmonic fill. Tempering, colors musical notes,- but the pure notes should be of theoretic interest. _____ chemistry: Electron spin in a single bond may be cis or trans (eg. beryllium) to the unbonded electron: This extra-stabilized spin (given its cross-atomic tie) may be record-able. A covalent electron orbital energy step might exist very close to an unbound electron orbital step in some nonuniform molecule where though the valence is normally closed, it might be charged to open by internal exchange (and produce a pn-type semiconductor), or conversely might be un-ionizable, isolating that energy step as orbitals vie for it. Its conduction-blinker version might oscillate within itself; Its un-ionizable version might transmit a "photon" only very slowly forward ... like some-called "slow glass". If energy were given to both 1-s electrons in a deep closed shell, they might hold that metastably because they can't emit, but eventually lopside and emit. Likewise, the 1-s deep-closed pair may hold a momentum angle, nutating, for long period; albeit nutation should slowly radiate by 'polar-charge-hole' emission, but unlike any ordinary photonwave for height and frequency ... more 'dark energy' .... _____ astrophysics: Lorentz Contraction: As an elemental particle approaches the natural-local speed of light, the leading front expresses a local-domain faster aether for the trailing back which then creeps forward in that local-domain, onto the leading edge: whence in sum apparently contracted ... aether-pressure and aether-speed is sufficient to push and keep the tail toward the head. Velocity and acceleration of mass-holes: The innards of black-hole 'mass-holes', though of slow innard-linear velocity, accelerate freely in a gravitational field applied externally, as the innards however small are yet mass, and that, mass-energy, though no longer atomic or nuclear, moving with the movement of massive objects and massless'ive photons at their there slower speed of light and gravity, readily cross-accelerate and turn-toward-forward, perpendicular to velocity, and adding energy crosswise, -as readily as before it slowed- ... It cannot be accelerated nor decelerated innard-forward or backward, than innard-light speed, but, turning to forward or backward, acceleration, is easy. The central mass may lag inside its mass-hole, a very short distance, but overall keeps-up till it reaches the real question: Can mass-holes travel near the speed of light in the external frame? Probably not, but the experiment might be to locate mass-holes related to galaxies at the redshifted edge of the cosmos, and check for less, redshift. Diffusion of neutron stars by charge-lifted spicules-tips reaching escape velocity. 'Acceleration Paradox' W = F·d on a circle, the force applied over short angular distance, moves a short centerward distance: W=Fd, but in fact also decelerates the same: the object changes direction only... correct the expression equation. Mass falling into a black hole 'exposes' behind an increased potential energy field that anything following can pick up... Hence the infalling mass is leaving behind some of its mass-energy (not particles but the total field)... hence things don't fall into a black hole but by reduction of mass-energy along the way in, a minuscule renormalized amount reaches the center: the hole mass is more outside than inside... The Special Relativity Twins' paradox is answered simply by the distance to the turnabout in the Earth-frame being measured as shortened in the Rocket-frame, and so takes less time to get there on the Rocket-clock... But, When the Rocket-twin looks at the Earth-twin's clock instead of the Rocket-twin's own already looked-at, the anomaly shows that the Earth-clock, though measured advancing slowing in the Rocket-frame, when looked-at, is found to have suddenly advanced: This anomaly is usually attributed to Time-advance/bias (cf the long-pole-in-the-short-barn-paradox) but such an advance means seeing the future of distant galaxies, by a leader in the Rocket-frame, but-yet to see that, the photons must have already arrived, but for another to declare it in the same -synchronized- frame is a simultaneity-mismatch in the Earth-frame: so making the 'god of physics true but every physicist a liar'... _____ quantum physics: [posted re a discussion of power MOSFET's 2012-02-15 1240 UT] When, Smart-Superconductivity...? A billion transistors per square inch, running parallel to get that 100mΩ-look... But the name, Transistor, trans-resistor, suggests defeat from the very start... When, are we electronics genius-types going to invent pseudo-superconductivity by simulating the properties of 'ordinary' superconductivity--? gangwavelength and quantum entanglement: this should be simple enough, bulk properties under extreme test, imposed by design under 'room' conditions... sub-nanometer stuff... digital approximation of a superconduction mode in silicon [semiconductor]--? Or simply, it's conduction in a nonconductor by entangled electrons hopping super-pad-to-super-pad. When two charged particles approach in a common-frame, one is presumed to produced a magnetic field the other sees, but-yet in the frame of either particle, the other is moving twice-as-fast and producing twice the magnetic field yet the first is not moving-through the field and should not feel the magnetic field, or, the first, not moving, produces no magnetic field and so the other, though moving, feels none, (or requires its own field to push itself). Now, the University Physics book (12th edition) admits this anomaly led to the discovery of the theory of Relativity, but does not do the simple mathematics for a lower-speed, (Relativity becomes measurably significant near the speed of light), And-yet such books have always given the first-order approximation, (cf the energy-of-motion ½ m v² is good enough to compute 2-place-accuracy up to 10% light-speed). Hence, magnetism is not understood in physics in the slightest--! It's still an anomaly, in the book... -BUT- We can resolve this somewhat: We need: the Local Value of the Universal Reference Frame, because-- In the particle frame, the Universe, is passing the other way, except-for that same particle: so, the moving charged universe produces a negative magnetic field of the opposite polarity-- meaning, the charged particle has its magnetic field right where it is, even standing still...! Now this may seem surprising, but we ought to run a space station experiment, multiply, with a superconducting shell repelling all magnetic fields from a charged particle amid Hall-effect devices measuring its Standing, Magnetic Field... and, secondly, we may need to compute ordinary magnetic fields as 'moving' in the universal reference frame as the magnetic field moves with its charged particle.... (This is just like the requirement in computing angular momentum: which also, needs the Universal Reference Frame....) A photon passing through a polarizer is forced to twist to the direction of the polarization... But physicists say it is not twisted nor forced but that its polarization-vector is separated into components and only one component passes and the other is absorbed, (typically)... yet the absorbed component is at an angle to the absorbing polarizer axis: it must be twisting and forced-so therefor... and furthermore light travels as photons which are not redshifted by polarizers, hence the photon must have been twisted, by force... and furthermore the photons that don't get through at all must be twisted the other way... but with a leftover. If an charged particle field is equivalent to a side-sliding magnetic field (integrated over a whole charge-flux-surface) then by the mathematician's Fixed Point Theorem 'Combing Hair On A Sphere' there must be at-least one 'cowlick' a direction without charge-field. An electron at a velocity has a wavelength, (likewise in quantum Simple-Harmonic-Oscillators), and so its probability-of-presence 'wave', times its charge, must be a singlesided wave, all negative or all positive, and so a Double-Slit Experiment should detect it at-most-only half-canceling. ____ bookbinding, script binding: (faster page-turning) Two-sided pages "doubled-back" numbered, righthand-and-backside: 1,3; 2,5; 4,7; 6,9; ... so that the page-sheet can be turned while reading the next, not waiting;- even keeping the last words at the bottom of the previous while starting the top of the next. Square-lock plastic-comb binding, narrow flat edge-profile (both back and paper edge), unlocks by turning to rhombus-diamond (making paper easier to thumbsnap, first half). (-aka- Recto-lock, for wider-back bindings.) _____ extras: Use(s) for the original Egyptian granite 'pyramids':
  • (Pharaoh/P'Ra-uk/'Ophra-ukh') The gold cap catches lightning to run down its rain-wetted slope-sides ...
  • (space-alien; pre-Pharaoh): Fill the central chamber with high-carbon oil-slurry and detonate a nuclear bomb above the gold cap: the fireball vaporizes the calcium-oxide-lime casings, compressing the sides inward: the overlapping granite blocks successively focusing the pressure inward to hundred times higher than the outer blast,-- condensing the carbon to a very large-kilotonnage diamond. (N.B. The outer downward vector reorients the inward force upward for central compaction.)
  • (Adam, Seth, Jared/Surid) Adam instructed Seth to build two columns-pillars, one of brick in case of world fire, one of stone in case of world-flood (the stone being the limestone casings which cannot withstand heat, and the brick unfired that cannot withstand water; the fire-or-flood-prediction was probably due to a nearby supernova);-- brick pyramids were unknown in early Egypt, but were-known in Sumeria: the zigurrats.
  • A polished pyramid reflects the view of passing clouds to,-or-from, the tip...
  • The limestone -casing- abundant of calcium, includes Ca-48 which, by extremely slow double-β-decay yielding a huge 4.3 MeV, should glow on overcast nights, or scintillate on-the-order-of maybe an average-'gray'-photon-per-second-per-cc...
  • On clear nights typical of a desert the polished pyramid is "full of stars..." _____
  • A premise discovery under the title,

    Grand-Admiral Petry
    ... cruising the cosmo-net on galaxy-planet Earth ...
    'Majestic Service in a Solar System'
    Nuclear Emergency Management

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