MATHOUGHTS NOTES

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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).
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edit keys: SEARCH forward, SKIP back, CUT back, DEPOSIT forward, REPEAT, RECALL
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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.
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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 ...
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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.
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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
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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
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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
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checkwriter:
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nomenclature terminology: deflection standard - deviation standard
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education problem set generation:

 - maximum distribution research: {NASA} data
 - high schools, colleges
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mathematics instructor:

 - question set generator
 - encyclopedia
 - grade
 - base tutoring
 - referencing
 - idea composition: hierarchy + cross-referenced
 - view magnification
 - reference path selection criteria/keying-actuation
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document similarity 'plagiarism' detection statistical rules (Cf word proximity)
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6-segment/bar numerals (based on written-8: 4-elbow, 7-top, 1-top, 1-bot, 2-bot, 3-knee)
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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
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other methods for propulsion:

electric acceleration in the solar system on the sun's thermionic charge
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digital treble-thread-gemming, HDDV projector

improve to HDTV now (television.html original concept)
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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 
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'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...)
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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,}

or

0 ≝ { }
1 ≝ {0}
2 ≝ {1} ≡ {{0}}
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deep space net:

vid-link communication
information
computation service
remote telemetry - DeepSpaceNet extension - delay-line

government surplus
government role needs
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font:

Q's-complement
Formal
halfspace (especially in monospace, Typewriter, etc.)
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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")
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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.
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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.
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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' ....
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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.

[already used] A mass falling into a mass-hole adds its momentum but to what--if
 speed stops inside a mass-hole, how can the infalling reach around to the other
 side to pull-it-forward as by 'dynamical friction' as there is nothing on-which
 to push-it-forward, and a central singularity would be too-small-to-contact, so
 the gravitational field itself, must have drag that is, the slowing,-gravity...
 perhaps the same as the power-limited-potential-mass-energy of the mass-hole...

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'...

It seems wise to also mention the meaning of 'argument' in mathematics, is-not, the
 'loud talk' despised by the-gods-themselves, also known as 'chutzpah' as when Cain
 decided that whereas Seth had decked him on the levee in Netet, he could no longer
 kill his younger brother, so he felt rehabilitated, and so returned to Sumer, from
 exile... likewise, proof-by-contradiction is not-merely saying-not-so, nor, saying
 proof-positive-my-contradiction-of-yours,-whatever, as when, 'precocious Einstein'
 conclusion-jumpers suggest time-travel may-be-possible because, his special theory
 relativity, discovered, so... (note that the disproof of his special relativity is
 by disproof of his assumption, of simultaneity, that-wherein assuming simultaneity
 exists, results in it not-existing for past-accelerated trains-and-frames-and-...)
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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.
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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.)
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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..."
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A premise discovery under the title,