Trix Question

Q:  How many non-Cooper Union Computer Engineers does it take to tune this system?
A:  All of them!
Ah.All, Again...
Q: And how many Cooper Union Computer Engineers do I need?
A: Just one, Hhheenryyyyy!

~~~~~~~~~~~~~~~~~

Ahem, St%*#; it's not gonna work if You throw your voice over other people--this morning it was Frank!
So, excuse me for being non-responsive by giving You the Silent Treatment.

Just like yesterday's, 'Are You Blind?'

I heard You project from one corner of the coffee shop on my way out of there.

Here's the answer back in case You are Deaf!

"No, I'm not blind! But I'm not Stupid, either!"

Oh! So, I now hear You callin' me a Genus!

I take it we can both finally move on, now that our short-lived mutual infatuation has worn off, unless You are envisioning some sort of inter-species interaction. Genus,  eh?

The modern human species comprises the only extant species of the genus - Homo sapiens; and now that I Am a Genus, (Genus, He Says!), by its very definition, that makes  Me the Alien!

An apt description, ar.  وصف  w.ss.f,  considering what this post is all about.

But all inanity aside, I will now attempt to describe  ( وصف) how information is never lost, only masked (it is preserved in the Zero Point Field).

And it only takes for someone to be well versed in a chosen area of interest to See It for What It Is--should one subscribe to Mr. Bremby's pseudo-randomness philosophy underlying motor vehicle license plates.

An attempt or demonstration on my part to illustrate as much since "He Indicates (Instructs/Demonstrates/Pictures) Using 119."

(BTW, thank You for the g'mmee ("For you," He said), it was so nice to see You the other evening  KIDR1--had we met prior to that occasion?)

Let's Pretend I AM A Quran Maven for the Purposes of This Example!

The possible combinations using the string triad 119, reading left-to-right, without transposing the numbers:

1; 1:1; 1:19.  11; 11:9.  119;

Surah 1 has only 7 Verses and there are only 114 Surahs in the Quran, leaving Chapter 1, Verse 1:1 and Chapter 11,  and Verse 11:9 as viable Surah and Sign substrings.

In the interest of saving Time and Space, I will only parse out the individual Signs and leave the whole Surahs for when I can devote more attention to this speculative realm than that allotted between dinner and bedtime, wield a staff of umpteen many, and have a wee bit more computing power than my MacBookPro can handle.

Surah 1 Al.Fatiha (The Opening Chapter)

بِسْمِ اللّهِ الرَّحْمـَنِ الرَّحِيمِ (1:1   
1:1 In the Name of God, The Gracious, The Merciful.

Surah 11 Hud (The Prophet Hud)
وَلَئِنْ أَذَقْنَا الإِنْسَانَ مِنَّا رَحْمَةً
ثُمَّ نَزَعْنَاهَا مِنْهُ
إِنَّهُ لَيَئُوسٌ كَفُورٌ (11:9  
11:9  And if We Impart to Humanity (Man) a taste (a modicum) of Mercy ( رَحْمَةً  Rahmatan) from Us
and then take it away from them (him);
they (he) abandon(s) all hope (despair)...blaspheme (forget Our Past Favor, revert to infidelity)

Then the possible combinations reading right-to-left, without transposing the numbers:

9;  9:1;  9:11.  91; 91:1.   911.

And, again, since there are only 114 Surahs in the Quran, 911 is not a viable Chapter number, leaving only Surah 9, Verses 9:1 and 9:11; and Chapter 91,  Sign 91:1 as usable substrings in this particular example.

Surah 9 At.Tauba (Repentance)
بَرَاءةٌ مِّنَ اللّهِ وَرَسُولِهِ
 إِلَى الَّذِينَ عَاهَدتُّم مِّنَ الْمُشْرِكِينَ (9:1
 9:1 God and His Messenger Absolve (hold guiltless) those you have made pacts with from among the pagans (idolators, infidels).

فَإِن تَابُواْ وَأَقَامُواْ الصَّلاَةَ وَآتَوُاْ الزَّكَاةَ
 فَإِخْوَانُكُمْ فِي الدِّينِ
 وَنُفَصِّلُ الآيَاتِ لِقَوْمٍ يَعْلَمُونَ (9:11
9:11 Should they repent, and gather to pray, and give to charity;
they are your bretheren in Faith.
And We Separate/Segregate/Partition/Adjudicate/Disentangle/Detail/Itemize/Partition/Spell out...نُفَصِّلُ the Signs (Quranic Revelation) to those who understand/can teach/are knowledgeable/for everyone to learn.

Surah 91 Ash.Shams (The Sun)
وَالشَّمْسِ وَضُحَاهَا (91:1
91:1 And the Sun and its Brilliance/sunshine/luster (var. waking, attention (shedding light on something), clarifies, explicates//its victims/sacrifices)

(If the triune was less than or equal to 114, it would be indicative of using that whole Surah to 'inform the field'; and the numbers do not necessarily have to be a triad, they could be quaternary or longer, as long as the string holds up to the numbering conventions in the Quran. For instance, Surah 17 has 111 verses, so a sequence of xxxxx digits could still make sense in this context, since Sign 17:111 exists, there is a Surah 111,  a Verse 11:17, 11:71, and other sensible substrings).

Taking all the above listed substrings for 119 and transposing Chapter:Verse --> Verse:Chapter yields:

1:1;  19:1;  9:11; 1:9; 11:9; and 1:91

The only viable additional substring to the set established so far is 19:1;

Surah 19 Maryam (The Virgin Mary)
كهيعص (19:1
19:1 kaf. ha. ya. 3'ayn. saad.

The series of 5 Muqati3aat,...  ص ع ي ه ك ...(K. H. Y. 3'ayn. Ssaadd)...

{Aside: added Nov 29, 2012--Good Morning,  Mr. אחד ויחיד  (or א,שהד was it? I can't read it, You Know, I go by pattern recognition).

Frazz Comic Strip
Pattern Recognition 'Really Really False'
Appeared in the January 13, 2013 Los Angeles Times

--isn't it a relief to finally do away with that thing behind Your ear, anyway? Isn't that much better now--so who cares why?  And I am happy to hear You don't care who she is, because You.Know.Who is still asking 'How does she look?'  I think to move things along quicker we should all start agreeing she looks 'good enough,' because just saying, 'beautiful' and 'gorgeous,' doesn't seem to cut it for Him. But, no matter what You all settle on for her looks, I want to be Independently Wealthy!}

Thanks! You heard right--I can be the gorilla in the window and You get to play at Ogee & Take me home--I could use some west and wee wax a shin, at last!

Moving right along...in Arabithmatic terms:

ص  = y

in complex analysis: ع = z = rÐj =   ل Ð ي

where:

ي  = φ (an angle)

ه = e (natural log base~2.718...)

ك = r dφ or κ (both the Greek kappa and the Arabic kaf have the same abjid/gematria value==20; so they have equivalence in scientific/arithmetic notation). Another take on what Kaf may mean, in addition to the modern accepted arithmetic usage, is Lam with a Hamza embedded in it: 
laam==ل

kaf==ك

hamza ==ء  which represents the variable d, or just as readily the operation d (derivative of  ل dφ );  r dφ

{I hear You. I am sure that You don't intend for me to feel the way I do about hearing you, but I can't help it...BTW, so far the sound checks out great! Can they find better applications for this than making it sound like they are following me around all over town? So, when is the persecution over?}

Back to the quirky math lesson...Just for You! (I know, I know; it's not what you asked for, need or want, but I will give it to You, anyway...How do You like that? So, by the same token, please explain why I keep hearing You say, "Just for you.")

First attempt when taking the Bludgeon approach is to make a direct substitution: (I make no representation other than I am guessing at this point & I realized once I got through the problem , I had left out the r in r (cos φ + i sin φ) term, so let's just assume r=1, as in a unit circle).

20~19:1   (e)(φ)  r( cos φ + i sin φ) y

Kaf= κ   is something like     Ha = (e) Ya =(φ) 3ay'n = z SSAAD= y

The Bludgeon Approach: direct substitution:  κ =(e)(φ) r(cos φ + i sin φ) y
assume φ is an angle (in radians) or variable t, the general form; (oops just realized the omission of r in the rÐj term, but rather than rework all this just pretend it's a Unit Circle, r=1)

and alternate form

has roots y= 0;  y =0  or t =0

and the 3D contour graph (mesh) looks like (thanks to wolframalpha.com):

That's right, a Flying Carpet!

Substituting 19:1 in the general form, for the variables in order (phi, or psi or t =19 and y=1):   yields     19 e^(1+i 19)(1)

alternate representation for which:

Note that z= 1, see ع above

...a transcendental number,  with the polar coordinates: 

r = 51.6474, φ = 8.61981 degrees--
what the angle value y = 8.61981 means:

it's an arc length along the Earth's equator of 596 miles (518 nmi, 960 km), 
an arc  length at 45 deg latitude of 422 miles (366 nmi, 679 km)

and correlates to:
~ 0.37 x the tilt of the Earth's axis relative to its orbital plane (~23 deg)
~2.2 x the tilt of the angle of the Leaning Tower of Piza (~ 4 deg)

interesting to note that the numeric value of r = 51.6474 correlates to:

~ 2.2 x  the tilt of the Earth's axis relative to its orbital plane (~23 deg)

____________________________________

By extension this same relationship κ =(e)(φ) r(cos φ + i sin φ) y and

in context with Surahs 13 Ar.Ra3d (Thunder) and 21 Al.Anbiya (Prophets), Verses 13:41 

and 21:44, respectively (the Quran as a Knowledge Object):

أَوَلَمْ يَرَوْاْ أَنَّا نَأْتِي الأَرْضَ نَنقُصُهَا مِنْ أَطْرَافِهَا 

وَاللّهُ يَحْكُمُ لاَ مُعَقِّبَ لِحُكْمِهِ وَهُوَ سَرِيعُ الْحِسَابِ (13:41 

بَلْ مَتَّعْنَا هَؤُلَاء وَآبَاءهُمْ حَتَّى طَالَ عَلَيْهِمُ الْعُمُرُ 

أَفَلَا يَرَوْنَ أَنَّا نَأْتِي الْأَرْضَ نَنقُصُهَا مِنْ أَطْرَافِهَا 

أَفَهُمُ الْغَالِبُونَ (21:44 

Both verses refer to shorting/reducing/making a gap or shortage نقُصُ in the 'Earth's' extremities, sides, tips, ends, parts or even parties (referring to folks/communities/people) طرف. 

In this case, the function (e)(φ) r(cos φ + i sin φ) y , shows a conspicuous 'clipping' or reduction of the corners in the imaginary contour plot for this function; a definite pattern that emerged when plugging the values 13, 21 or 19 in for the y term, and on cursory examination, the results seem to point to an apparent threshold at values >=9: 

Such that: 13 (e)(φ) r(cos φ +/- i sin φ), or 19 (e)(φ) r(cos φ +/- i sin φ) or 21(e)(φ) r(cos φ +/- i sin φ) produced these type of 3D contour plots:

Imaginary Contour Mesh f(t) = 21 e t r (cos t + i sin t) from 19:1 Muqati3'at
Corners Reduced Per 13:41 and 21:44
Compare to 'Flying Carpet' Above

Imaginary Contour Mesh f(t) = 13 e t r (cos t - i sin t) from 19:1 Muqati3'at
Reduced or Showing Gap at Extremities (parts, corners) Per 13:41 and 21:44
Compare to 'Flying Carpet' Above

________________________________________

A second approach: 
Assuming the derivative form of κ  as  κ' =(e)(φ)r(cos φ + i sin φ) y

For a Unit Circle, the general equation and solution are:

i e.,  k'(φ)) =e(φ) z y == e (φ)(cos φ + i sin φ) y

An ordinary first-order differential equation

the solution for which:

If the radius is not equal to 1 the differential equation  k'(φ) =eφr(e^iφ) *y yields the following general solution:

for simplicity, stick to the unit circle, and keep r =1 st: κ'(φ) = e φ (e ^(iφ))y

then

k(φ) = c1 +[e^(iφ)](e- i*e*φ)y

this function returns a complex solution:

 c1 = k(φ) ,   φ  = -i


and a real solution:


c1 = k(φ) - ye, φ = 0



Interesting, more so, since setting k(φ) = 0, produces a trace c1 reminiscent of the Time Equation, by choosing y carefully:

since c1 = - e^i(φ) [ e - e i φ] y

See Time Equation
Superposition of Sinus Curves
Sine and Cosine

----

Sound Check: I hear 'awesome' 'awesome' 'ahhh, sum?"--STOP. Who are you foolin'? I have clearly demonstrated I can't even do high school math, unless you mean Genius, like Daffy Duck, who happens to be a Super Genius!--Just make it easy for me and simply tell me what everyone else does at this level, I will follow suit.

{Honestly, I know You hear me go off on All of You when I get home--evidenced by how what I say in my bathroom at home is in the next morning's syndicated cartoon strip, and You still tittering about 'my wife is gorgeous', 'beautiful', 'genius'---&amp..?}

Non Sequitur Comic Panel
Gorgeous-Like the Grand Canyon~Whilst Gorging On Grapes
Appeared in LA Times Dec 1, 2012

As for You/Him/'We Never been introduced' asking, 'Did you miss me?" 

I don't know, let me hurl the nearest projectile in Your general direction and see by how much! 
Is that where the first flying saucers came from?

And I am an unmarried woman, so who, if it's me You are alluding to, am I married to? 
Am I a polygamist without my knowing? If it turns out I am still married to my ex in some reformulated format then i can only assume I am in Hell for all eternity and will keep up the silent treatment because I choose not to acknowledge such injustice in my life And hereafter.

That is not to say that I will not take You up on your proposed 'cover marriage' just so my daughter can get that Father she always wanted to spoil her rotten like the princess she deserves to be--never saw anyone work harder than she since such a young age to impress her dad just to have his behavior make me sign on to the 'all men are a!@#@*%s' philosophy.}

Why it matters concerning what this Blog goes on and on and on about (decipher in context):

• In graph theory, the connectivity of a graph is given by κ.
• In differential geometry, the curvature of a curve is given by κ.

Right-Hand Side of the Equation
Definite and Indefinite Integrals

How this is applicable to 19:1: 
The most general interpretation of the series of muqati3'at based on the above:

¶ (r e ^{^± i θ}) = e*θ *(rcos θ ±  rsin θ) *y

Left Hand Side of the Equation
Partial Derivatives and Complex Map
Note the Analogy between the Complex Map and Sett Point Paper

Since here we are considering curvature the most general interpretation of the right-hand side of the equation may not be a straight multiplication, but makes sense in the context of curve parameters:
ie. x, y , and z (meaning the pitch (as in the case for a helix), or simply a third axis (as is the case for azimuth)):

x (t) = a cos (t)
y (t) = a sin (t)
z(t) = bt

st;

x (θ)= rcos θ
y (θ)=±  rsin θ
z (θ) = ey θ, where y may be an actual constant value, like 1 or 19, or substitute the y(θ) from the y coordinate, so that  z1(θ) = e*(±  rsin θ)*θ...

Assuming a right-handed circular helix with radius 1, and pitch 2pi*b = 2pi (ey) and using cylindrical parameters [r, θ, h] :
r (θ) = 1
θ (t) = t
h (t) = (et)*t =e(t^2)  which seems appropriate in this case since t^2 is analogous to (sin^2 θ); the square of the sine of an angle, essentially the concept of spread in rational trigonometry, or it may possibly still mean et?)

Several interpretations follow:

Parametric Plots v Unwrapping Curves v Sign 19:1

Ichthus v Solar Geometry and Sign 19:1

Parametric curve of the form x = rcos t,  y = r sin t, and z = e*t* y(t);
Here z(t) = e t sin (t)  the crumpling is mitigated near the Origin, where there is 'no crookedness'  (See Sign 20:108)

Parametric curve, Cylindrical coordinates of the form x = 1,  y = t, and z = e*t;
Here the contour maps show no curvature at all, (See Sign 20:107)

Parametric curve of the form x = 1,  y = t, and z = e*t^2;
Here z(t) = e t^2  the flats and the 'mountains/barrows' depicted int the above alternative parametric curves are now sunken due to the emergent parabolilc function z= et^2, or 'bottoming' at the Origin,  (See Sign 20:105)

Superimposed Sinusoids

Surah 88 Al.Ghashiya (The Overshadowing)
أَفَلَا يَنظُرُونَ إِلَى الْإِبِلِ كَيْفَ خُلِقَتْ88:17
وَإِلَى السَّمَاء كَيْفَ رُفِعَتْ (88:18) 
وَإِلَى الْجِبَالِ كَيْفَ نُصِبَتْ (88:19) 

وَإِلَى الْأَرْضِ كَيْفَ سُطِحَتْ (88:20) 
فَذَكِّرْ إِنَّمَا أَنتَ مُذَكِّرٌ (88:21   
....
88:17 Do they ever Consider (See) Rainclouds (الْإِبِلِ, al.abili, borrows from the root a.b.l.h, to be full/wet/forerunner and when put together= rainclouds, or even 'pregnant camel', but in context, it makes more sense if the root is أبله, abl.h, meaning vacant/vacuity/emptiness/gap/space/vapor and var. sod, adj., inanity, vacuum/senselessness, what we would call a 'void') and how they are (it is) Created?
88:18 And the Sky (Heavens) how they are Raised (Elevated)
88:19 And the Hills (Mountains) how they are Erected
88:20 And the Earth how it is spread out (ssutihhut)
88:21 So Remind (them) for you are a Reminder.

Surah 87 Al.A3la (The Most High, Ultimate Power)
سَنُقْرِؤُكَ فَلَا تَنسَى 87:6
87:6 We Recite It (Teach It) to you so that you do not forget.

• In physics, the torsional constant of an oscillator is given by κ as well as Einstein constant of gravitation.
• In structural engineering, κ is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical elastic moment of an unbraced steel member.
• In electrical engineering, κ is the multiplication factor, a function of the R/X ratio of the equivalent power system network, which is used in calculating the peak short-circuit current of a system fault. κ is also used to notate conductivity, the reciprocal of resistivity, rho.
• In chemistry, the compressibility of a compound is given by κ.

"What's Wrong?" He wants to know. Here, here, I'll s-p-e-l-l it out for ya so we're all on the same page and we all know what' wrong.

Generalized Gas Compressibility Chart
Note: Isotherm at 20% Compressibility

The Generalized Gas Compressibility Chart above is an example of a generalized compressibility factor graph derived from hundreds of experimental PVT data points of 10 pure gases, namely methane, ethane, ethylene, propane, n-butane, i-pentane, n-hexane, nitrogen, carbon dioxide and steam. Note behavior at z=20% (compressibility factor at a reduced pressure ~1 and that these gases are associated with oil well lighters) and gases used to develop the isotherms which model near ideal gas behavior and what is in a can of one particular air freshener. 

A less harsh, read less harmful approach, would be to use a benign real world model on deteriorated brains rather than such a toxic exposure to healthy brains.

Need I say more, my math may be questionable, but I think I got the chemistry right--in a nutshell the implication is deliberate and malicious intent to cause harm. 

To which He follows with, "تأكد 085", which means 'be certain', 'ensure' or 'confirm'; Surah 85 Al. Buruj (The Zodiac)-- to the best of my ability, I confirm they are still in the Sky and I got burnt. 

and Sign 08:5--
Surah 8 Al.Anfal (The Spoils of War)

كَمَا أَخْرَجَكَ رَبُّكَ مِن بَيْتِكَ بِالْحَقِّ
 وَإِنَّ فَرِيقاً مِّنَ الْمُؤْمِنِينَ لَكَارِهُونَ (8:5
8:5 Even as Your Sustainer brought you forth from your home in Truth, although a segment of the Believers were averse to it (disliked it). 

That would be True, both instances.

• In psychology and psychiatry, kappa represents a measure of diagnostic reliability.
• In biology, kappa and kappa prime are important nucleotide motifs for a tertiary interaction of group II intron.
• In biology, kappa designates a subtype of an antibody component.
• In pharmacology, kappa represents a type of opioid receptor.
• Kappa statistics such as Cohen's kappa and Fleiss' kappa are methods for calculating inter-rater reliability.

Upper-case letter Κ is used as a symbol for:

• In set theory, kappa is often used to denote an ordinal which is also a cardinal.

--------------------------------

{Addendum: Dec. 4, 2012, so I am to have a sense or get a feel  حس  for 3:79 and 37:9, just in case I missed it. 

Surah3 Al.3'mran 

مَا كَانَ لِبَشَرٍ أَن يُؤْتِيَهُ اللّهُ الْكِتَابَ وَالْحُكْمَ وَالنُّبُوَّة 

ثُمَّ يَقُولَ لِلنَّاسِ كُونُواْ عِبَادًا لِّي مِن دُونِ اللّهِ 

وَلَـكِن كُونُواْ رَبَّانِيِّينَ بِمَا كُنتُمْ تُعَلِّمُونَ الْكِتَابَ 

وَبِمَا كُنتُمْ تَدْرُسُونَ (3:79  

 3:79 It's not likely (apt, possible) that a person whom God has Granted Scripture and Wisdom and the Prophethood that he should afterwards say to people, 'Serve me instead of god.' But (what he said was), "Be faithful servants of the Lord by virtue of your constant teaching of the Scripture and of your constant study thereof."

And from 

Surah 37 As.Saffat (Rangers)

إِنَّا زَيَّنَّا السَّمَاء الدُّنْيَا بِزِينَةٍ الْكَوَاكِبِ (37:6) 

وَحِفْظًا مِّن كُلِّ شَيْطَانٍ مَّارِدٍ (37:7) 

لَا يَسَّمَّعُونَ إِلَى الْمَلَإِ الْأَعْلَى وَيُقْذَفُونَ مِن كُلِّ جَانِبٍ 37:8) 

دُحُورًا وَلَهُمْ عَذَابٌ وَاصِبٌ (37:9

37:6  Indeed, We Bedecked (Adorned) the Worldly Sky with the beauty of the planets 

37:7 And (they serve as a) Security from every titanic devil (rebellious demon). 

37:8 They cannot hear anything but the Higher Chiefs (Congregation), and they will be pelted/ejected/liabled/slandered/defamed/flung from every direction (side). 

37:9 Stopped (Repulsed), for theirs is a perpetual persecution. 

I don't have to defend myself here, I already covered this almost at the inception. I never took any of this lightly, and the tragedy of it is that I know I wasn't invited to the dance, and I didn't want to come along, either.  

That's why what they did is harram, and I took every measure I could to prevent it from reoccurring--to me or any one else. 

I take it my recently sampling this first hand is just to be sure, but I never contested it and hopefully this hazing will let up as quickly as it set in. I don't believe I am such a titan, but the only rebellion You'll see in me is if I am forced to wake up to that a!@#@*%s--One time through that shi1112 is enough. 

I heard my daughter on the bus today. And my brother in the locker room, and my Dad, someone calling my Mom 'Um Ahmad'. I pretty much know the whole family made it.
So, I take it this reminder is for 'them thar others' edification.

...And my friend Francis keeps cropping up everywhere I plan to be...

Harmonica Player
Black and White Charcoal Sketch
Artwork by Japie Goosen 2011

What makes me so special?

I find myself asking myself the very same question.

But my Mother answers me so I don't sound so crazy..."You know, dear, they didn't want a 'virgin', they wanted to read this version--you always had a problem with your annunciation!"

(She thinks it's part and parcel with my poor spelling).

 Here's one example:

Surah 55 Al.Rahman
مُدْهَامَّتَانِ (55:64 
Nearly all accepted translations take this to mean:
55:64 (Gardens, from the context) 'dark green' (in color or of foliage)

And this is my understanding of the same verse Sign 55:64 based on my 'annunciation' (that's right, that would make me a lousy Catholic, too!)
55:64 Its Range Extensive (the maximal range, enduring/endurance interval/or gap...)

Then use Sign 55:64 as angles or velocity/angle or some such combination to maximize the Range! That's if we're talking projectiles (or mystery of alpha).}
----------------------

TiraMissU

Torus Knots (Planar)

As long as the world is turning and spinning, we're gonna be dizzy and we're gonna make mistakes. --Mel Brooks 

Rotational Matrix Take II

Tommy's Interwoven Paths In His Past and Present Life
In His Home
Raiding His Father's Refrigerator
I See Him Standing by the Fridge
His Father Said the Pot Flew Out of a Pantry Kitty-Corner to the Fridge During a Crisis Some Time Later
His Kitchen Is Just About Square
And Tommy's Path Seems to Be On a Diagonal , His Orientation Turned Around

I take it Yous guys are less than impressed with my arithmetic derring-do, since yer all so focused on her looks (not my looks, her looks, because I'm not supposed to take it personally).

Based on the above Scenario, our brave young soldier Tommy goes into his kitchen (at his father's house) just days before he was supposed to report to boot camp for deployment to some vacation spot.

Like any other young man, he goes through the kitchen door and heads due East to raid the refrigerator.

Surely there must be something to eat!

Some time after, Tommy dies of dehydration because his drill Sergeant couldn't allow a break for water during a strenuous exercise before ever getting deployed. Which causes Tommy's father a great deal of distress, and makes his good friend wonder 'what is it about men that makes them act like accomplished women?'

And during a pivotal moment in his father's coping mechanism failure, a sauce pot comes flying out of the NW pantry of the kitchen (no earthquakes reported in that part of town on that particular occasion) and lands right in the middle of the square kitchen (6 ' x 6').

Determine the rotational matrix based on the above scenario.

 (A bad drawing to kind o' confuse the issue (the planes are offset along a central axis, much like a helix/screw threads/or augers), think 3D and not certain the time).

{"Sit on it...and Rotate!"--The Fonz (Henry Winkler), popular 1970'a sitcom Happy Days

The Rotational Matrix

In Euclidean geometry, a rotation is an example of an isometry, a transformation that moves points without changing the distances between them. 

Rotations are distinguished from other isometries by two additional properties: 

1. they leave (at least) one point fixed, and 
2. they leave "handedness" unchanged. 

By contrast, a translation moves every point, a reflection exchanges left- and right-handed ordering, and a glide reflection does both.

A rotation that does not leave "handedness" unchanged is an improper rotation or a rotoinversion.

A geometric rotation transforms lines to lines, and preserves ratios of distances between points. A rotation is a linear transformation of the vectors, and can be written in matrix form, Qp. 

The fact that a rotation preserves, not just ratios, but distances themselves, it follows that...

Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, all these properties may be summarize by saying that the n×n rotation matrices form a group, which for n > 2 is non-abelian. 

Called a special orthogonal group, and denoted by SO(n), SO(n,R), SOn, or SOn(R), the group of n×n rotation matrices is isomorphic to the group of rotations in an n-dimensional space. 

This means that multiplication of rotation matrices corresponds to composition of rotations, applied in left-to-right order of their corresponding matrices.

To rotate points in the xy-Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian coordinate system use a rotation matrix R; each point is represented by a column vector v, of each point's coordinates (position). The rotated vector is then obtained by matrix multiplication Rv. 

Rotation matrices are square matrices (nxn), with real entries; characterized as orthogonal matrices with determinant 1.

The special orthogonal group SO(n) is the set of all such matrices of size n, generally not commutative.

Improper rotations, characterized by orthogonal matrices with determinant -1 (instead of +1) combine proper rotations with reflections (which invert orientation). 

The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. -90°).

Basic rotations:

Three basic (gimbal-like) rotation matrices rotate vectors about the x, y, or z axis... 

All other rotation matrices can be obtained from these three using matrix multiplication. 

...to represent a rotation whose yaw, pitch, and roll are α, β, and γ, respectively. 

...whose Euler angles are α, β, and γ (using the y-x-z convention for Euler angles).

Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis (Euler rotation theorem).

There are several methods to compute an axis and an angle from a rotation matrix one is based on the computation of the eigenvectors and eigenvalues of the rotation matrix. It is also possible to use the trace of the rotation matrix.

...which shows that  is the null space of... 

Viewed another way, [] is an eigenvector of R corresponding to the eigenvalue; every rotation matrix must have this eigenvalue.

To find the angle of a rotation, once the axis of the rotation is known, select a vector  perpendicular to the axis. Then the angle of the rotation is the angle between__and__.

It is much easier to calculate the trace (i.e. the sum of the diagonal elements of the rotation matrix)...

In three dimensions, for any rotation matrix , where a is a rotation axis and θ a rotation angle,

 (i.e.,  is an orthogonal matrix)

 (i.e, the determinant of  is 1)

 (where  is the identity matrix)

The eigenvalues...

The trace of  is  equivalent to the sum of its eigenvalues.

Some of these properties can be generalized to any number of dimensions. In other words, they hold for any rotation matrix...

Ambiguities:  Alias and alibi rotations

The interpretation of a rotation matrix can be subject to many ambiguities.

The change in a vector's coordinates can be due to a turn of the coordinate system (alias) or a turn of the vector (alibi). Any rotation can be legitimately described both ways, as vectors and coordinate systems actually rotate with respect to each other. Here, the alibi approach is used to describe rotations. 

The vector can be pre-multiplied by a rotation matrix (Rv, where v is a column vector), or post-multiplied by it (vR, where v is a row vector). Here rotations are produced by means of a pre-multiplication.

The vector space has a dual space of linear forms, and the matrix can act on either vectors or forms.

In most cases the effect of the ambiguity is equivalent to the effect of a transposition of the rotation matrix.

Two features are noteworthy: 

1. First, one of the roots (or eigenvalues) is 1, i.e., some direction is unaffected by the matrix. For rotations in three dimensions, this is the axis of the rotation (a concept that has no meaning in any other dimension). 
2. Second, the other two roots are a pair of complex conjugates, whose product is 1 (the constant term of the quadratic), and whose sum is 2 cos θ (the negated linear term). This factorization is of interest for 3×3 rotation matrices because the same thing occurs for all of them. (As special cases, for a null rotation the "complex conjugates" are both 1, and for a 180° rotation they are both −1.) Furthermore, a similar factorization holds for any n×n rotation matrix. If the dimension, n, is odd, there will be a "dangling" eigenvalue of 1; and for any dimension the rest of the polynomial factors into quadratic terms like the one here (with the two special cases noted). Its a given that the characteristic polynomial will have degree n and therefore n eigenvalues. And since a rotation matrix commutes with its transpose, it is a normal matrix, so can be diagonalized. 

Every rotation matrix, when expressed in a suitable coordinate system, partitions into independent rotations of two-dimensional subspaces, at most n⁄2 of them...

The sum of the entries on the main diagonal of a matrix is called the trace...

The large number of options is possible because rotations in three dimensions (and higher) do not commute. 

Reversing a given sequence of rotations results in a different outcome. 

This implies that two rotations cannot be composed by simply adding their corresponding angles; i.e., Euler angles are not vectors, despite a similar representation as a triple of numbers. 

} 

(The rest of us just spin on our heels and walk a distance about 6Ö2 along the diagonal heading WNW if we think we are at the fridge or ESE if we think we are at the pantry and want something out of the fridge.

Or become really well acquainted with quaternions to get a sense for what Tommy was seen doing in his 'spare time'. )

Like I said, some people say, 'Thank You,' and some people can be quite demonstrative of it.

Just like those 'I love you' tokens I been hearing of late.

If You Love Me, you would stop this (You Know Exactly what I mean).

Surah 2 Al.Baqarah (The Calf)
وَلاَ تَقُولُواْ لِمَنْ يُقْتَلُ فِي سَبيلِ اللّهِ أَمْوَاتٌ
 بَلْ أَحْيَاء وَلَكِن لاَّ تَشْعُرُونَ (2:154

2:154 And do not say of those slain in God's Cause that they are dead;
Nay, they Live and yet you perceive it not.

I know, I know, it must be End of the World because i am the smartest girl in the room; don't anybody panic because God can make another dysfunctional one just like it!

I Think I Hear My Mother Calling...

...and, Boy! Does He Sound Mad!

A dog comes when he is called, but a cat takes a message and will get back to you later.--Mary Bly

{PS: Things could not have gone any worse for me up until 6 months ago, then they absolutely plummeted and now I have to put up with more angst inducing weirdness and take it on the chin?
--nuh-uh!
I hear these guys mumbling "beautiful" and "who is she" and some say "she's my mom" and some say "she's my wife". 

And sometimes to actually hear my name called!--one guy in particular seems to have lost his wife and is searching high and low for her--the bus, the train, any restaurant I happen to randomly pop into--so much stress to have to hear about it and hold down a meal or catch the next bus while all this is going on...
(I am not 'the wife' in the biblical sense, since I see him go home to his real wife, he just flies in for the day, does some work and goes back home to her; I am a 'working girl', the worst kind ever, the type that actually does not get paid for a job well done! ergo~GOD, and the need for One!)

Still my second rate life; where most girls get to age to perfection and 'beautiful' to them means 'timeless', for me that kind of remarkable beauty translates to 'dateless'--or am I mis.hearing 'beautiful' for 'pitiful'?
Besides, there's no shortage of beauty in the world, just a lack of clean public restrooms and frequent LA Metro buses that run on time.
What's more, as I read this entry to edit it, I am watching this really pretty young woman (a classic beauty, like Venus) outside a coffee shop shedding a stream of tears and it just reinforces what I have known all along, Beauty is not an Armor impervious to being pierced by Sorrow. 

And do You mean I don't get to kick back and play "Can You Tag (Finger) Malcolm"  (the adult version of "Where's Waldo") forever hereafter--I thought I was on some level of the death plane (heaven, hell, earth2,3, 4...); or tell jokes to myself once I get home (i.e., haunt the house; a step up for me-- that type of behavior was limited to the kitchen in real life)?

I know this is not any kind of love story, the last thing I would be looking for, assuming I do get to the threshold of heaven, would be a 'husband', so that begs the question, 'Have we caught the culprit(s), yet?' I  soo need a vacation! (and at this rate the interest alone you all owe me for backpay must be astronomical--so the sooner we settle this the better).

Great (10/18/2012/..so that's how it is Dad, 'hello' n 'good-bye' n 'you ditch, too?!' it's not like I can't hear You telling bro # 2 and bro #3 'it's your sister'!! If You all insist on this routine, then make it so I don't have to hear yous guys.}

On The Subject of Name Calling

Using functional magnetic resonance imaging (fMRI), brain activation patterns were examined in response to hearing one’s own first name in contrast to hearing the names of others. There are several regions in the left hemisphere that show greater activation to one’s own name, including middle frontal cortex, middle and superior temporal cortex, and cuneus. 

These findings provide evidence that hearing one’s own name has unique brain functioning activation specific to one’s own name in relation to the names of others. 

(Hi, Norman--You wouldn't be Swedish, by any chance?)

On Hearing Your Name Called 
& Putting The Conspiracy Theories To Rest

There are several instances of reputable people (of the non-psychotic variety) hearing voices and responding to them prior to the historical development of electronic PsyOps type weapons (microwave, brain enhancement (ie. air freshener), etc.) development.

In recent history, there is such an instance described by Mother Teresa which led Her to what became Her life's mission in India.

She, being a faithful person, did not question the Voice as anything other than being patently genuine and the Voice of some Agency of God, (God, an Angel, my Mom in her kitchen?), and did not run around trying to locate the source like the rest of us would by first typing in some keywords into our favorite online search engine.

And prior to the advent of such emergent technology, there is evidence that this sort of thing has been going on for quite some time, and Say What!--no modern technology required?

A Smattering of Selected Case Studies In The Bible

Isaiah 43:1
And now, thus said Jehovah, Thy Creator, O Jacob, and thy Fashioner, O Israel, Be not afraid, for I have redeemed thee, I have called on thy name -- thou art Mine.


Isaiah 45:3
I will give you the treasures of darkness, riches stored in secret places, so that you may know that I am the LORD, the God of Israel, Who summons you by name.

Yet, with the advent of technology (the Internet) and information from questionable sources (like bloggers and Fox News) for unverified reasons (disinformation and to hang on to their money) it becomes necessary to figure out what may or may not be a viable call from a legitimate caller (Holy God and Company).

How to Suss Out Whether It's A Higher Power 

or 
Steve at the US Army Signal Corps Doing the (Name) Calling...

1. God is Responsive to the caller and can help

Surah 2 The Calf

 وَإِذَا سَأَلَكَ عِبَادِي عَنِّي فَإِنِّي قَرِيبٌ 

أُجِيبُ دَعْوَةَ الدَّاعِ إِذَا دَعَانِ 

فَلْيَسْتَجِيبُواْ لِي وَلْيُؤْمِنُواْ بِي

 لَعَلَّهُمْ يَرْشُدُونَ  (2:186 

2:186 And if My Servants Ask You (the Prophet, pbuh) about Me (God), Truly, I Am Near; I Respond to the call of the caller, whenever they call. So, have them answer (respond) to Me and Follow Me, that they may be guided aright.

2. The Caller Calls you by your Name or Gives you a name of some significance (non-derogatory). 

(Figure on a planet of xxx billion people, what are the odds? What makes you so famous to attract Steve's attention?)

• Examples of those hearing the call are called by name and sometimes even Named by the Caller:

Surah 3 The Family Al.3'mran

فَنَادَتْهُ الْمَلآئِكَةُ وَهُوَ قَائِمٌ يُصَلِّي فِي الْمِحْرَابِ

 أَنَّ اللّهَ يُبَشِّرُكَ بِيَحْيَـى مُصَدِّقًا بِكَلِمَةٍ مِّنَ اللّهِ وَسَيِّدًا

 وَحَصُورًا وَنَبِيًّا مِّنَ الصَّالِحِينَ  (3:39  

3:39 So the Angel Called (Zachariah) while He was praying in the Sanctuary, "Indeed, God Blesses you with Yahya ("He Lives"==John, the first time the name John/Yahya had been proferred on anyone). He (John) will Affirm His (God's) Words Truthfully; And He (John) will be outstanding among men, and chaste, and a Prophet among the Righteous.

Surah 19 Maryam (Mary)

يَا زَكَرِيَّا

 إِنَّا نُبَشِّرُكَ بِغُلَامٍ اسْمُهُ يَحْيَى

 لَمْ نَجْعَل لَّهُ مِن قَبْلُ سَمِيًّا (19:7    

19:7 (The Angel called,) "O, Zachariah! We, indeed, bring You tidings of a son (young soul, ghulm) whose Name is Yahya (John the Baptist); We have never given this name to anyone before Him."

Surah 20 Ta.Ha

فَلَمَّا أَتَاهَا نُودِي يَا مُوسَى (20:11 

20:11 Once He (Moses) neared it (the fire in the desert), He was Called, "O, Moses!"

Surah 37 Those Ranged (by Rank, Echelons, Arrayed)

وَنَادَيْنَاهُ أَنْ يَا إِبْرَاهِيمُ  (37:104 

37:104 And We Called Him, "That You Are Ibrahim!"

Surah 79 Al.Nazi3at

إِذْ نَادَاهُ رَبُّهُ بِالْوَادِ الْمُقَدَّسِ

 طُوًى (79:16 

79:16 When His Sustainer Called Him In the twice-hallowed Valley, Tuwa. 

(Alternatively, 'If  His Sustainer Calls him (his servant) in the holy wadi (a glen, a narrow dry river bed), "Tuwa!"~ 'Double!' or 'Fold' or 'Double Back!'; var. phonetically 'It's You!'?)

3. Those hearing the call are God's Servants (Moses, Elijah, Isma3yliya, the Faithful, Believers), and the Muslims are called first.

Surah 30 Romans

وَمَا أَنتَ بِهَادِي الْعُمْيِ عَن ضَلَالَتِهِمْ

 إِن تُسْمِعُ إِلَّا مَن يُؤْمِنُ بِآيَاتِنَا

 فَهُم مُّسْلِمُونَ (30:53

30:53 And You (the Prophet, pbuh) cannot guide the blind out of their darkness; 

only such as believe in  Our Signs can hear, for they are Muslims (Submit to God's Will).

4. The Mechanism to Call and/or hear the Caller is Primordial, it should require no man-made (synthesized) technology, since it is stipulated that God has already spoken to not only Adam and the Prophets, but some of Adam's offspring before the Last Day.

Surah 7 The Heights (Al.a3raf)

وَإِذْ أَخَذَ رَبُّكَ مِن بَنِي آدَمَ

 مِن ظُهُورِهِمْ ذُرِّيَّتَهُمْ

وَأَشْهَدَهُمْ عَلَى أَنفُسِهِمْ أَلَسْتُ بِرَبِّكُمْ

قَالُواْ بَلَى شَهِدْنَا

 أَن تَقُولُواْ يَوْمَ الْقِيَامَةِ إِنَّا كُنَّا عَنْ هَذَا غَافِلِينَ  (7:172  

7:172 And, indeed, God Takes from B'nai Adam (Adam's Offspring), 

and from the seed of their issue,  

and We Swore them (had them bear witness) by their own Souls, "Am I Your Sustainer?" 

They said, "It is True, we swear that indeed." 

So that on the Day of Judgment (Resurrection) you (Adam's issue) cannot claim  (say that) you were unaware (that being the case).

5. A Description That Such a Natural Mechanism Does Exist 
(that's why it's wrong to tamper with people and make them think otherwise)

• Yet, there is a barrier that cannot be breached, except for special circumstances (like Death/Wrongful Death/Premature Death/Martyrdom/etc.) or by special agencies (like Angels).  

• The concept limbo tries to explain such a mechanism; in the Arabic it is referred to as barzalch or the veil.
• barzalch, the Barrier that separates the worlds (the veil)--Angels are used to convey messages between the worlds (can breach the barrier). 
• some say that it is a spacetime where the Soul lingers between planes of existence (ie., as it travels from plane-to-plane/ level-to-level/ tier-to-tier between earth, heaven and hell) for some unspecified period of time (usually understood to mean after one's death; younger generations familiar with first person player games may be more comfortable with it having come across the concept of 'levelling up' like in World of Warcraft).  

• It would seem, and it must be taught, that Heaven and Earth coexist both spatially and temporally.
• And that they are co-mingled, but we are unaware of that being the case when we are born as infants and have a conventional life on Earth... (Don't panic! It's not the first time I played matchmaker!! Something I choose to do to fill this time with since You.Know.He.Who doesn't want me to 'run with the pack,' heh, heh--snark.)

Surah 35 Fatir (The Originator, Creates Something from Nothing)

يَا أَيُّهَا النَّاسُ 

اذْكُرُوا نِعْمَتَ اللَّهِ عَلَيْكُمْ  

 هَلْ مِنْ خَالِقٍ غَيْرُ اللَّهِ 

يَرْزُقُكُم مِّنَ السَّمَاء وَالْأَرْضِ 

لَا إِلَهَ إِلَّا هُوَ فَأَنَّى تُؤْفَكُونَ (35:3  

(35:3) O, People (Nas, All of Creation)!

Remember God's Provisions (Bounty) He Graces you with.

Who is it that can Create it, other than God, Providing you from (both) Heaven and Earth. 

There is no God other than He. 

How is it you turn from this Truth?

• The understanding is that while God provides us with benefits from heaven as well as earth, the boon of God's Grace does not trickle down to those considered to be in hell (ie., a low moral level of existence).

Surah 7 Al.A3raf (The Heights)

وَنَادَى أَصْحَابُ النَّارِ أَصْحَابَ الْجَنَّةِ

 أَنْ أَفِيضُواْ عَلَيْنَا مِنَ الْمَاء أَوْ مِمَّا رَزَقَكُمُ اللّهُ 

قَالُواْ إِنَّ اللّهَ حَرَّمَهُمَا عَلَى الْكَافِرِينَ (7:50  

 7:50 And the denizens of the fire (Hell) call to the denizens of the garden (Heaven, Eden), "Please pour over us of that water or whatever God Provides (Blesses) you with, but they say, "Indeed, God Forbids These to the Unfaithful (Nonbelievers, Deniers).

• Apparently sound works just fine between the tiers/planes of existence through the barrier, that's why the sobriquet Isma3el (He Can Hear God, or God Heard him/her), since there is an allusion that there are those already at the cusp?   who can be heard calling out (7:46).

 Surah 7 Al.A3raf (The Heights)

وَبَيْنَهُمَا حِجَابٌ

 وَعَلَى الأَعْرَافِ رِجَالٌ يَعْرِفُونَ كُلاًّ بِسِيمَاهُمْ

وَنَادَوْاْ أَصْحَابَ الْجَنَّةِ أَن سَلاَمٌ عَلَيْكُمْ

لَمْ يَدْخُلُوهَا وَهُمْ يَطْمَعُونَ   (7:46 

7:46 And Between (them) is a Veil (Barrier  حِجَابٌ),
and on the Heights (Al.A3raf) are Men who know everyone by their marks (their names  بِسِيمَاهُمْ) 
and they call the denizens of Heaven, "Truly, Peace Be Upon You!" 
They have not yet entered it, and they long to.

{Sign 7:46 is made all the more interesting in that the Men (rijln  رِجَالٌ) calling from this transitional state (limbo, barzalch, al.a3raf)  through the barrier (veil حِجَابٌ) are aware of they're being in such a state and there is text to support the fact that these men desire to transcend it to a better state (Heaven) and moreover that they have an assurance of it, but for whatever reason they have to be in this suspended intermediate state (arrested development?) for a term. (I can't think of any other reason for this other than to get to watch everyone else rediscover electricity!) 

The fact that the text expressly states that they are Men, explains why my presence here is unexpected, unwanted,  not welcome, and...Surprise!

The implication is that these are good men, based on the reputation of those known to have been inducted into such a service in the past--I give Yous Guys, Solomon, and no, He was not happy to see me hear/here, either!

38 Suad ص

(38:32 فَقَالَ إِنِّي أَحْبَبْتُ حُبَّ الْخَيْرِ عَن ذِكْرِ رَبِّي
 حَتَّى تَوَارَتْ بِالْحِجَابِ

(38:32) And (Solomon) He said, "Truly do I love the love of good, in remembrance of my Sustainer,"- even as (He was) hidden behind the veil...}

• The understanding is that this suspended state, like an arrested development, akin to a hibernation, falls upon certain individuals all of the sudden, without them having any indication when and if it happens to them or even if they are in it at all. Surah 36:9 gives a further description:

Surah 36 Ya.Seen 

وَجَعَلْنَا مِن بَيْنِ أَيْدِيهِمْ سَدًّا

 وَمِنْ خَلْفِهِمْ سَدًّا

 فَأَغْشَيْنَاهُمْ فَهُمْ لاَ يُبْصِرُونَ (36:9   

36:9 And We Closed Off (Sddna) what is between their hands (their present, what they are currently doing) and of what is behind them (what they had done in the past) Closed Off (Sddna), And (in this manner) We Veiled them while they were Unaware.

(Surah 36:9 is metaphorically speaking of giving closure to something, or finality to whatever it was they were doing or had done in the past while they were taken into this Veiled existence, unawares. (One recent example is how I was not supposed to notice how my morning prayer was interrupted right after the first rack3a last Sunday Oct. 20, 2012 (but that's why I get confused about the date/time)). Read Sedna legends of the Native Americans, and the Recent sighting of Sedna in Orbit, and the Phoenix Lights Incidence of 1997, and note the word Sedna is a homophone for  the Arabic word meaning 'closure' or 'pay-back'.)

6. The qualities of those hearing the call and why they know themselves to be legitimate:

(Look, I am not posing as any of them, I am merely interpreting the text based on my understanding of it as of 2012 CE and the prism of my personal life experience).

• Only certain humans while alive can fathom it (truly understand it and clearly distinguish a call coming through the veiled existence (be it coming over/through the heavenly, earthly or hell levels). The two cases being Prophets and Enlightened Ones (like the Dalai Lama)...a marginal third case, the contemporary 'Men In Black'.

• Only the Living can hear 

Surah 35 Fatir (The Originator)

وَمَا يَسْتَوِي الْأَحْيَاء وَلَا الْأَمْوَاتُ 

إِنَّ اللَّهَ يُسْمِعُ مَن يَشَاء 

وَمَا أَنتَ بِمُسْمِعٍ مَّن فِي الْقُبُورِ (35:22       

(35:22) They are not equal (the same), the Dead and the Living. 

Indeed, God Makes to Hear (Listen) whomever He Wills; 

and You (the Prophet, the Messenger) cannot make to hear those who are in their graves.

• And those who can hear, must be open or receptive to the Message:

Surah 27 Naml (Ants)

إِنَّكَ لَا تُسْمِعُ الْمَوْتَى وَلَا تُسْمِعُ الصُّمَّ الدُّعَاء إِذَا وَلَّوْا مُدْبِرِينَ (27:80  

27:80 Truly, You (the Prophet, the Caller) cannot make the dead hear nor make the deaf to listen 

(the deaf being those refusing to hear the message, not merely unable to hear with their ears) 

to the call while they are fleeing from You. 

(lit, have their backs turned to you, oppose you, 

var. while they are 'being played'~orchestrated/contrived)

• Only those with the faculty of discernment are valid callers:

 Surah 7 Al.A3raf (The Heights)

وَنَادَى أَصْحَابُ الأَعْرَافِ

 رِجَالاً يَعْرِفُونَهُمْ بِسِيمَاهُمْ 

قَالُواْ 

مَا أَغْنَى عَنكُمْ جَمْعُكُمْ وَمَا كُنتُمْ تَسْتَكْبِرُونَ   ( 7:48

7:48 And the inhabitants of al.a3raf call ( الأَعْرَافِ , rt   عْ رَ فِ    literally, 'knowing'--those possessed with the faculty of discernment/understanding/knowing).

Men who know them (those being called) by their names (marks).

Saying, 

"Of what benefit to you is all you have amassed, or your arrogance?"

• And, again, there is no mistaking Who is Calling and Via what Agents (Agency).

 Surah 14 Ibrahim (Abraham)

قَالَتْ رُسُلُهُمْ أَفِي اللّهِ شَكٌّ فَاطِرِ السَّمَاوَاتِ وَالأَرْضِ

 يَدْعُوكُمْ لِيَغْفِرَ لَكُم مِّن ذُنُوبِكُمْ وَيُؤَخِّرَكُمْ إِلَى أَجَلٍ مُّسَـمًّى

 قَالُواْ إِنْ أَنتُمْ إِلاَّ بَشَرٌ مِّثْلُنَا

 تُرِيدُونَ أَن تَصُدُّونَا عَمَّا كَانَ يَعْبُدُ آبَآؤُنَا

 فَأْتُونَا بِسُلْطَانٍ مُّبِينٍ   (14:10  

(14:10) Their Messenger said to them (his people), 

"Do you doubt that God, the Originator of Heaven and Earth, Is Calling you to forgive you (shield you) from your sins (wrongs) and to grant you a reprieve (delay/defer) for a named (determined) term (period of time). 

They say, "Indeed, you are merely a man like us who wants us to repulse that which our forefathers worshipped (held dear), so show us a Clear Authority (your valid authorization to do so)."

{And I been hearing it and I beg to differ, I never made any representation of my being God, since a middle aged old lady with asthma and shin splints and a spotty period, is none such...interpretive dance (barzalch) as provided.}

7. To Determine the Validity of the Caller (Who Is Calling) and why the Call:

• Historically the Valid callers give information, in real time to the called, and the information is relevant; they identify themselves and those they call, and the reason for being summoned (3:39)

• Maryam (pbuh) is led to water in the desert:

Surah 19 Maryam (Mary)

فَنَادَاهَا مِن تَحْتِهَا

 أَلَّا تَحْزَنِي

 قَدْ جَعَلَ رَبُّكِ تَحْتَكِ سَرِيًّا (19:24   

(19:24) Then He (The Angel) called Her (Maryam, Jesus's Mother) from beneath (the palm tree), 

"Do not grieve (dispair), 

Your Sustainer Has Made a Rivulet run beneath you (under your feet)."

• Those compelled to call on God are given relief (He both Calls and Hears His Servant's Calls):

Surah 27 Naml (Ants)

أَمَّن يُجِيبُ الْمُضْطَرَّ إِذَا دَعَاهُ 
وَيَكْشِفُ السُّوءَ 
وَيَجْعَلُكُمْ خُلَفَاء الْأَرْضِ 
أَإِلَهٌ مَّعَ اللَّهِ 
قَلِيلًا مَّا تَذَكَّرُونَ (27:62  

(27:62)  Or (Who Is It) Answers (Responds) to the Call of the one compelled (coerced, forced) to call on Him;
And Uncovers (Reveals) Misdeeds (var. Rids them of evil, ills, maladies that beset them);
And Made you viceroys upon the Earth?
Is there a god other than The One True God (Allah)?
How little you consider (remember)!"

• The Caller (In this case, God) Clearly Identifies Himself to Moses, whom He calls by name:

Surah 28 Qasas (Stories)

فَلَمَّا أَتَاهَا

 نُودِي مِن شَاطِئِ الْوَادِي الْأَيْمَنِ

 فِي الْبُقْعَةِ الْمُبَارَكَةِ مِنَ الشَّجَرَةِ

 أَن يَا مُوسَى

 إِنِّي أَنَا اللَّهُ رَبُّ الْعَالَمِينَ (28:30 

(28:30)  As He (Moses) neared it (the fire in the desert),
He Was Called, from the Right Bank of the Wadi (dry river bed)
In the Hallowed Valley from the Tree,
"Truly,  Moses,  I Am God--The Sustainer (Lord) of the Worlds."

• The Speaker/Caller (Gabriel) gives Muhammed (pbuh) information He could not have known specific details about Moses' encounter with God (28:42-28:48) and let's Him know exactly why He is being called:

Surah 28 Qasas (Stories)

وَمَا كُنتَ بِجَانِبِ الطُّورِ 

إِذْ نَادَيْنَا

 وَلَكِن رَّحْمَةً مِّن رَّبِّكَ 

لِتُنذِرَ قَوْمًا مَّا أَتَاهُم مِّن نَّذِيرٍ مِّن قَبْلِكَ 

لَعَلَّهُمْ يَتَذَكَّرُونَ (28:46  

(28:46)  And You (Muhammed pbuh) were not present on the side of The Tur (Mount Sinai)
When We Called (Moses)
Yet it is a Mercy from Your Sustainer
That You Warn A Community (People) Not Given a Warner Before,
So That They May Bethink Themselves (Use Their Reason).

• One reason for the renewed call is for clarity/illucidation, to benefit the living (like technological advancement) and to allow it to be broadcast among those who never heard it before, again, meant to be of some benefit to them. 
• It is never the case that it is a New Message, it can be text as Torah, Testament (Injeel) or Quran or some other Holy Scripture, the Message Originates from One Source, so no surprise here.

Surah 36 Ya.Seen

وَمَا عَلَّمْنَاهُ الشِّعْرَ

 وَمَا يَنبَغِي لَهُ 

إِنْ هُوَ إِلَّا ذِكْرٌ

 وَقُرْآنٌ مُّبِينٌ (36:69   

(36:69) And We Do Not Teach Him (the Messenger) Poetry, 

nor does He (the Messenger) excel in it (it is not proper/meet for Him) .... 

Truly, it serves as a Reminder, 
and An Evidentiary Recitation 
(meant to Clarify various things, in Science, Law, Civility, Medicine, etc.)

لِيُنذِرَ مَن كَانَ حَيًّا

 وَيَحِقَّ الْقَوْلُ عَلَى الْكَافِرِينَ (36:70  

36:70 To Warn those who are Living 
and to Renew (Verify) the Message (the Call) to the Unfaithful 
(Non Believers--those not having heard the Message before).

• To inform the one being called of God's Forgiveness (or Displeasure, serve to check someone's behavior):

Surah 2 Al.Baqara (COW, Calf, Heifer)

فَتَلَقَّى آدَمُ مِن رَّبِّهِ كَلِمَاتٍ 

فَتَابَ عَلَيْهِ 

إِنَّهُ هُوَ التَّوَّابُ الرَّحِيمُ (2:37 

(2:37) And Adam Received Words from His Sustainer (Lord)

That He Forgave Him (God Relented toward Adam);

For, indeed, He Teaches/Accepts Repentence (At.Tawab) , He Is The Merciful (Al. Rahheem).

• If the reason for the Call is not immediately obvious, it only means that it may have come a little too early (or in one isolated case, I think the information got destroyed in transit).

Surah 10 Yunus (Jonah)

وَيَقُولُونَ لَوْلاَ أُنزِلَ عَلَيْهِ آيَةٌ مِّن رَّبِّهِ 

فَقُلْ إِنَّمَا الْغَيْبُ لِلّهِ 

فَانْتَظِرُواْ إِنِّي مَعَكُم مِّنَ الْمُنتَظِرِينَ (10:20

(10:20) And they say, "Why has there not been sent a (grand/spectacular) Omen from His Lord?" 

Say, "Only God Knows the Unseen (Or, basically, 'Here it is, you all just don't get it!); so, be patient (wait for it), I, too, anticipate it (I'll wait right along with you)."

8. There are Proper Times to Hear/Respond to the Valid Call and/or Caller.

• Valid Callers know the Propriety/Protocol when calling; they Do Not call if someone is in their 'private' apartments 49:4. 

Surah 49 Hujurat

إِنَّ الَّذِينَ يُنَادُونَكَ مِن وَرَاء الْحُجُرَاتِ 
أَكْثَرُهُمْ لَا يَعْقِلُونَ (49:4    

49:4 Indeed, those calling You from behind the Hujurat (Your private apartments),
most of them are childish (ill-behaved, not sensible, unreasonable).

9. The Consequences of Making a Pretense of either Being a Legitimate Caller (either God or a Prophet) or posing as having heard a valid call, or falsifying the validity to a Sanctified Message, just may be worse than death.

Surah 11 Hud

وَمَنْ أَظْلَمُ مِمَّنِ افْتَرَى عَلَى اللّهِ كَذِبًا 

أُوْلَـئِكَ يُعْرَضُونَ عَلَى رَبِّهِمْ وَيَقُولُ الأَشْهَادُ هَـؤُلاء

الَّذِينَ كَذَبُواْ عَلَى رَبِّهِمْ

أَلاَ لَعْنَةُ اللّهِ عَلَى الظَّالِمِينَ (11:18   

(11:18) And who can be more in the dark/oppressive (lost) than those who invent a lie about God; and when they are brought before their Lord and the Witnesses say, "These are they who lied about God, and such oppressors incur God's Condemnation."

Surah 6 Cattle (Al.An3am)

وَمَنْ أَظْلَمُ مِمَّنِ افْتَرَى عَلَى اللّهِ كَذِبًا

 أَوْ قَالَ أُوْحِيَ إِلَيَّ 

وَلَمْ يُوحَ إِلَيْهِ شَيْءٌ 

وَمَن قَالَ سَأُنزِلُ مِثْلَ مَا أَنَزلَ اللّهُ 

وَلَوْ تَرَى إِذِ الظَّالِمُونَ فِي غَمَرَاتِ الْمَوْتِ 

وَالْمَلآئِكَةُ بَاسِطُواْ أَيْدِيهِمْ 

أَخْرِجُواْ أَنفُسَكُمُ الْيَوْمَ تُجْزَوْنَ عَذَابَ الْهُونِ بِمَا كُنتُمْ تَقُولُونَ عَلَى اللّهِ غَيْرَ الْحَقِّ 

وَكُنتُمْ عَنْ آيَاتِهِ تَسْتَكْبِرُونَ (6:93

(6:93) Who can be more lost/in the dark/oppressive than someone who ascribes to God a lie,

 or claims, "This has been Revealed to me (from on High)," 

and nothing has been revealed to them.

To whomever says this, Say, "Perpetuate (Reveal) anything the like of what God Reveals!"

And if You can only see these lost (souls) during the throws of death,

when the Angels shackle their hands/restrain them by their hands, 

(Saying), "Out with your souls (this may be an idiom for 'they will make them confess)! Today you will earn (what you merit), severe punishment (chastisement) for that which you were ascribing to God without sanction,

and were derisive of His Signs (Messages)!"

Surah 40 Ghaffir

الَّذِينَ كَذَّبُوا بِالْكِتَابِ 

وَبِمَا أَرْسَلْنَا بِهِ رُسُلَنَا 

فَسَوْفَ يَعْلَمُونَ (40:70

(40:70) Those who belie Our Book (falsify the Quran, or disbelieve Sacred Scripture) and that which We Send with Our Messenger...they shall soon Know It (to be the Evident Truth and despair for not having learned during life, read in context 40:68-40:72).

• Just so there is no misunderstanding as to what it is we consider The God around here & clearly it is not some guy or gal in a coma!

Surah 14 Ibrahim (Abraham)

أَلَمْ تَرَ أَنَّ اللّهَ خَلَقَ السَّمَاوَاتِ وَالأَرْضَ بِالْحقِّ 

إِن يَشَأْ يُذْهِبْكُمْ وَيَأْتِ بِخَلْقٍ جَدِيدٍ (14:19)

14:19 Can you not see that God Created the Heavens and the Earth in Truth (with an Inner Truth); indeed, If He Wills He Can Replace you (Trades you in) to Bring About A New Creation.

وَمَا ذَلِكَ عَلَى اللَّهِ بِعَزِيزٍ (14:20  

(14:20) And this is not any difficulty for God.

• Satan calls, too--can't help anyone and cannot harm the faithful (those who believe the Truth), and in general, doesn't have any real information to share (like the code to my Swiss bank account or the address to my new house next door to Yours (Nice is nice).

Surah 114 An,Nas (People, Communities, Creation)

مِن شَرِّ الْوَسْوَاسِ الْخَنَّاسِ (114:4  

(114:4) (I seek refuge in God) From the Evil of the Whisperer who subdues 

(with what he is heard to whisper~a psychotronic weapon of a sort? 

don't know my name? 

thinks I'm pretty?

sneaks up on me in the restroom to demonstrate the cloaking device I gave him;

my kids knew better and stopped doing that the minute they could bus themselves.
--Okay, to be fair, it was the kitchen and He did thank me for the cloak.)

Surah 14 Ibrahim (Abraham)

وَقَالَ الشَّيْطَانُ لَمَّا قُضِيَ الأَمْرُ 

إِنَّ اللّهَ وَعَدَكُمْ وَعْدَ الْحَقِّ 

وَوَعَدتُّكُمْ فَأَخْلَفْتُكُمْ 

وَمَا كَانَ لِيَ عَلَيْكُم مِّن سُلْطَانٍ 

إِلاَّ أَن دَعَوْتُكُمْ فَاسْتَجَبْتُمْ لِي 

فَلاَ تَلُومُونِي وَلُومُواْ أَنفُسَكُم 

مَّا أَنَاْ بِمُصْرِخِكُمْ وَمَا أَنتُمْ بِمُصْرِخِيَّ 

إِنِّي كَفَرْتُ بِمَآ أَشْرَكْتُمُونِ مِن قَبْلُ 

إِنَّ الظَّالِمِينَ لَهُمْ عَذَابٌ أَلِيمٌ (14:22

(14:22) And Satan says, once the order is carried out (God Decides-- the matter is decided/order is executed), "Truly, God Promised you a Truthful promise, and I promised you and deceived you (var. to oppose you, supplant you, fell back on my promise to you);  and I had no power over you except that I called you and you answered/responded to me. So, do not blame me, but blame yourselves (your own selves/souls). I didn't cry out to you and it's not for you to cry out to me. 
I do not believe in (reject) whatever you associate with me from before (that you espouse to me previously that I have any share in God's Dominion).
Indeed, the (real) oppressors have earned a severe punishment (to be tortured)."
(On a personal note, I do not condone torture).

Surah 11 Hud

فَإِن لَّمْ يَسْتَجِيبُواْ لَكُمْ 

فَاعْلَمُواْ أَنَّمَا أُنزِلِ بِعِلْمِ اللّهِ 

وَأَن لاَّ إِلَـهَ إِلاَّ هُوَ 

فَهَلْ أَنتُم مُّسْلِمُونَ (11:14

(11:14) And when (your false gods) fail to respond to you (cannot answer you), then know that this (Quran) is Revealed to you with God's Sanction (Knowledge); and that, Truly,  there is no other deity except for Him. 
So, when will you submit (to Him)?

• Why my confusion about this sad state of affairs...41:44 why in the Arabic language--(See Not Much of a Poker Face):
• While I can no longer feign being clueless, the fact remains that I really don't understand how an unfortunate 'industrial accident' evolved into this much clarity, but initially, the writing did help take my mind off the monstrous headache. 
• But, I now think the grievous suffering that caused was the coercive force that made this come about, and that's why I still think it was never intended for me to publish this--but I never got to say good-bye to my kids and was hoping somehow Word would get back to them.
• All that and Arabic is not my primary spoken language.
• And, I am not a Man--Hu-man, Wom(b)-man, but not a guy.

Surah 41 Fussilat

وَلَوْ جَعَلْنَاهُ قُرْآنًا أَعْجَمِيًّا 

لَّقَالُوا لَوْلَا فُصِّلَتْ آيَاتُهُ أَأَعْجَمِيٌّ وَعَرَبِيٌّ 

قُلْ هُوَ لِلَّذِينَ آمَنُوا هُدًى وَشِفَاء 

وَالَّذِينَ لَا يُؤْمِنُونَ فِي آذَانِهِمْ وَقْرٌ 

وَهُوَ عَلَيْهِمْ عَمًى 

أُوْلَئِكَ يُنَادَوْنَ مِن مَّكَانٍ بَعِيدٍ (41:44  

(41:44) Had We Made (Brought) the Quran in a foreign language (Farsi, African, alien language); 
they would say, "Why have the Signs been imparted in a foreign (alien) language, and He (the Prophet) is an Arab?
Say, "It (the Quran/Recitation) is for the Believers (serves) as a Guidance and a Source of Health (Well-being).
As for those who do not believe, there is a deafness in their ears;
and to them it's obscure (they are blind to it)."
It's like calling them from a far away place (remote place--like the Planet Seddna!).