An Affine-ity of Sorts

The Preamble/(sick to my stomach today anyway so this is a fitting reminder):

Surah 10 Yunas (Jonah)
قُل لَّوْ شَاء اللّهُ 
مَا تَلَوْتُهُ عَلَيْكُمْ وَلاَ أَدْرَاكُم بِهِ
 فَقَدْ لَبِثْتُ فِيكُمْ عُمُرًا مِّن قَبْلِهِ أَفَلاَ تَعْقِلُونَ
(10:16)

(10:16) Say, "If God Willed I would not have brought it (The Quran) to you and you would not have known anything of it, and I dwelled amongst you a Lifetime before (I brought it). Will you not use your Reason?"

{Aside: There are some out there who think I took it upon myself to do this, when the fact is that I did not volunteer and I know it's not my place to do so and I tried my best to avoid it. Sign 10:16 is eloquent in stating how this is not just in my head, it's all in my past. Which begs the question, what am I still doing here?}

Algorithms exist which can track critical distance from a moving plane point P (ie, where You are when You visit the Orange Field) to a static smooth curve (ie, where You Originate/Are Projected from,  be it the Blue or Gray field), without resorting to global search strategies beyond initialization (ie, so You do not get lost in space and always know the starting point).

An ordinary Cusp
on the Curve
x^3–y^2=0

Such an approach involves detecting transition events associated with the point's perturbation and successfully dealing with annihilation or creation events.

Annihilation/creation is one and the same event temporally speaking.
The one You experience depends on where You happen to be 'standing, (ie., Your Point of View/Perspective), basically the position associated with the perturbations at the transitions.

In order to avoid global searches for critical distances once such transitions are encountered, and at such transitions or various curve discontinuities (ie., like if You find Yourself at the cusp of a logocycle or saddle point in space), You can travel through it because...

U.R.IBIN (ie., My 'Son'-- 'Of Me'--):

Surah 3 Al.3'mran (Jesus' Family Name,'3mran)
قَدْ خَلَتْ مِنقَبْلِكُمْ سُنَنٌ
فَسِيرُواْ فِي الأَرْضِ
 فَانْظُرُواْ كَيْفَ كَانَ عَاقِبَةُالْمُكَذَّبِينَ  (3:137

3:137 We Created Generations/Orders/Aeons before (We Created) you, so travel (course) throughout the Earth and Observe/See the outcome of the deniers (those who falsify the truth/liars)

Surah 6 Al.An3'am (Cattle, Chattle...Property)
قُلْ سِيرُواْ فِي الأَرْضِ 
ثُمَّ انظُرُواْ كَيْفَ كَانَ عَاقِبَةُ الْمُكَذِّبِينَ 
(6:11)

6:11 Say, "Travel (set a course) throughout the Earth and then look (consider) the outcome/the end of the deniers (those who falsify the truth/liars).

Surah 9 Tauba (Repentance)
فَسِيحُواْ فِي الأَرْضِ أَرْبَعَةَ أَشْهُرٍ 
وَاعْلَمُواْ أَنَّكُمْ غَيْرُ مُعْجِزِي اللّهِ وَأَنَّ اللّهَ 
مُخْزِي الْكَافِرِينَ
(9:2)

(9:2) Travel freely (fluidly/flux) throughout the Earth four months and know (learn) that you cannot escape (frustrate) God and that God confounds the unfaithful.

Surah 16 Nahl (Bees)
وَلَقَدْ بَعَثْنَا فِي كُلِّ أُمَّةٍ رَّسُولاً أَنِ اعْبُدُواْ اللّهَ وَاجْتَنِبُواْ الطَّاغُوتَ
 فَمِنْهُم مَّنْ هَدَى اللّهُ وَمِنْهُم مَّنْ حَقَّتْ عَلَيْهِ الضَّلالَةُ 
فَسِيرُواْ فِي الأَرْضِ فَانظُرُواْ كَيْفَ كَانَ عَاقِبَةُ الْمُكَذِّبِينَ (16:36)

16:36  And in the past We Sent/Raised In every nation a Messenger (Saying): "Follow/Worship God and avoid idolization (false imagery)." Some of them were Guided unto God and some of them increased in their misguidance/straying, so travel freely (fluidly/flux) throughout the Earth and see/observe how the deniers/liars ended up.

Surah 27 Naml (Ants)
قُلْ سِيرُوا فِي الْأَرْضِ 
فَانظُرُوا كَيْفَ كَانَ عَاقِبَةُ الْمُجْرِمِينَ   
(27:69)

27:69 Say, "Travel (course) through the Earth and see/observe what became of the criminals/miscreants/guilty.

Surah 29 3'ankabut (Spider)
قُلْ سِيرُوا فِي الْأَرْضِ فَانظُرُوا كَيْفَ بَدَأَ الْخَلْقَ
 ثُمَّ اللَّهُ يُنشِئُ النَّشْأَةَ الْآخِرَةَ 
إِنَّ اللَّهَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ
(29:20)

29:20 Say, "Travel (course) throught the Earth and see/observe how God originates the Creation and then Brings Forth the Emergence of the Hereafter (Its Consequence/Maturation). Indeed, God Has Power Over Everything (Is Capable of Anything)."

Surah 30 Romans (Ar.rum)
قُلْ سِيرُوا فِي الْأَرْضِ 
فَانظُرُوا كَيْفَ كَانَ عَاقِبَةُ الَّذِينَ مِن قَبْلُ
 كَانَ أَكْثَرُهُم مُّشْرِكِينَ
(30:42)

30:42 Say, "Travel (course) through the land (throughout the Earth) and look/discern (be able to make a distinction/differentiate) the final outcome of those who before were mostly heathens (idolators/pagans/those who associate anything else with the One True God).

It is important to point out the emphasis is for the Believers to travel freely (set a course + flux) and make careful observation (look to see) in order to be able to even distinguish or discern that the Creation and Recreation (Hereafter) is indeed taking place in situ and that the Creation is not as static as we may be duped into thinking.

Apparently, there is little chance of encountering or being able to gauge a fold in space/time if restricted within a narrow physical existence. So, for some who do not venture more than 20 miles beyond where they were first born, this may not be a concept they can readily assimilate, let alone detect given their circumspect movement on the Earth.

And as such, what we are on about here (tay-el-ard), may seem like weird science.

The more widely-travelled set, however, may be able to relate to at least some of these concepts having merit beyond the occasional honorable mention in fairy tales.

Given Vectors defined by Chapter:Sign:Word Location  سِيرُوا   'seeru'  'Travel':

3, 137, 6  (alif, lam, mim)
6, 11, 2  (non muquati'at)
16, 36, 24 (non muqati'at)
27, 69, 2  (tta, sin)
29, 20, 2 (alif, lam, mim)
30, 42, 2 (alif, lam, mim)
and
9, 2, 1 (non muqati'at)  ('Travel' given as سِيحُواْ   ' seehhu' so this particular Sign may or may not be part of the vector space considered here) 

First square matrix taken in chapter ascending order where the word 'Travel' appears in the same location, ie, word number==2:
27, 69, 2 (tta, sin)
29, 20, 2 (alif, lam, mim)
30, 42, 2 (alif, lam, mim)

Matrix: {{27,69,2},{29,20,2},{30,42,2}}
Determinant: 186
Eigenvalues: 70.4771; -21.3535; -0.12359
Trace: 49 =[1 + cos (t)] = [cos (t) = 24]

sin^-1 (24) = ~  3.87077i (r=3.87077, theta = 90degrees) ~1.2321 pi

Second square matrix taken in chapter ascending order and share the same muqati'3at == alif.lam.mim.:
3, 137, 6 (alif, lam, mim)
29, 20, 2 (alif, lam, mim)
30, 42, 2 (alif, lam, mim)

Matrix: {{3, 137,6},{29,20,2},{30,42,2}}
Determinant =3850 (positive, eigenvectors have same orientation, product of the eigenvalues have same sign as the Determinant; the higher the value of the Determinant, the more valuable the information)
Eignevalues: 78.3513; -52.4138; -0.93749 (positive eigenvalues (real part) mean solution spirals away from the origin; negative eigenvalues (real part) mean solution spirals towards the origin; purely imaginary eigenvalues mean the solution neither spirals in or out from the origin but circles around it)
Trace = 25 = [1+ 2 cos (t) ]== [cos (t) = 12]


           sin^-1 (12) =  ~  3.17631i (r= 3.17631, theta = 90degrees) ~1.011 pi

Matrix Trace is related to Group Character; the Trace of Marix A, TrA, is the sum of the diagonal elements of a matrix; and the Trace is the sum of the eigenvalues of the matrix. The Determinant, detA, is the product of the matrix eigenvalues. For the case where TrA=0, detA=0, or (TrA)^2= 4detA the system is not structurally stable, ie., a small change in the entries of matrix A will destroy this property. Other cases are structurally stable, i.e., if the system has a sink, any nearby system will have a sink.

The Matrix A can be considered to be a Point in the
Determinant-Trace Plane
If the Determinant is Negative it is A Saddle point (one positive and one negative solution).
If the Determinant is Positive, eigenvalues have the same sign as the Trace
For the degenerate case where the detA=0, solutions are constants.
Comprehensive eigenvector ray paths explanation and movie.

Arithmetically, transition events are related to singularity and catastrophe theories.

The Swallow Tail's - Series on  Catastrophes
Oil on Canvas 1983 by Salvador Dali

(apparently some of ewes guys have already tried this vector math and that's why you've been popping in and out of public restrooms...but I'll do the math exercise just the same...)

Diagram of cusp catastrophe: 
Brown and Red curves show  x satisfying dV/dx = 0 for parameters (a,b), 
are drawn for parameter b continuously varied over several values of parameter a. 
Outside the cusp locus of bifurcations (blue), 
for each point (a,b) in parameter space there is only one extremising value of x. 

Two different values of x, giving local minima of V(x) for each (a,b), 
are possible inside the cusp, separated by a value of x giving a local maximum.

René Thom's catastrophe theory:

Thom suggested that in four-dimensional phenomena, there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": fold, cusp, swallowtail, butterfly, hyperbolic umbilic, elliptic umbilic, and parabolic umbilic. 

"The shape of Dalí’s Swallow’s Tail is taken directly from Thom’s four-dimensional graph of the same title, combined with a second catastrophe graph, the s-curve that Thom dubbed, "the cusp". 

Thom’s model is presented alongside the elegant curves of a cello and the instrument’s f-holes, which, especially as they lack the small pointed side-cuts of a traditional f-hole, equally connote the mathematical symbol for an integral in calculus.--wikipedia 

This may not seem of any valuable interest in real-world dynamics, unless you are truly observant.

For example, to the uninitiated, a drive along the freeway is a chance to go fast and burn some gas. A side benefit to which is that it is the closest a human being can get to actually flying. More so than in airplanes since the travel compartment is pressurized so the actual sensation of flight is insular at best.

In a moving car and with the windows down the feel of the wind rushing by and the traction against the road causes the experience to be more proximate to the real thing our fine feathered friends take for granted.

What has all this to do with cusps and bifurcations?

The beauty of the pragmatic application is in its subtlety. Because not only is God the Devil in the Details, but God is Imperceptible/Subtle, leaving the bludgeon approach to people like Me.

The fortunate few, who think 'forwardup' is a direction, are attuned to this happenstance occurring more commonly than one would think; to everyone else 'it's just another stack of hay.'

Those aware of the details of how such a catastrophic cusp event occurs in practice can see that while maintaining a constant speed along with the flow of other highway traffic, and all other parameters being the same, they begin to notice their vehicle either pulling away quickly from the field behind them or that they may see themselves dropping back away from the field of traffic ahead of them inexplicably fast, despite no changes in acceleration.

Magic! Or you happen to hit a fold in the road, not a bump, not a pot hole.

For the majority of us, we tend to notice what song is on the radio more than any such phenomenon.

And then we act vacant, obtuse and clueless when the same phenomena occur on a much larger scale like that of the Bermuda Triangle 'disappearances.'

An ordinary Cusp formed by the Optical Caustic
formed by light rays at the bottom of a tea cup.

The plane curve cusps are all diffeomorphic to one of the following forms: x2 − y2k+1 = 0,
where k ≥ 1 is an integer.

Algorithms have also been established that track point-curve critical distances exactly on piecewise smooth curves, deriving algebraically the unfolding formulas for degenerate critical distances (ie., to make it easier for me to find You because when it comes to Math and Science, I am a little retarded--not necessarily a self-depricating bad thing since by the time it occurs to me just how angry I should be, the problem is resolved and I just have to convince myself all there's left to do is wait for the dust to settle).

Sort...Cycle...Fold...and other Possible Outcomes at Catastrophic Events 

(and we're not talking just laundry, here):

Surah 15 Hijr (Rocky Tracts, have many sharp edges or Cusps)
إِنَّ رَبَّكَ هُوَ الْخَلاَّقُ الْعَلِيمُ (15:86

15:86 Indeed, Your Lord Is The Omniscient Creator!

Argyle Sweater
Forgotten Tools

وَلَقَدْ آتَيْنَاكَ سَبْعًا مِّنَ الْمَثَانِي وَالْقُرْآنَ الْعَظِيمَ (15:87

15:87 And We Have Given You 7 of the mathanee (traditionally interpreted to mean Surah 1 Al Fathha (The Opening) which is 7 of the most often repeated verses; literally,   الْمَثَانِي  means 'the folded, enfolded, pleated, flexions, folds and/or 'that which folds or causes to fold/bend') and The Quran Al.3'attheem (Magnificent, Sublime, while  عَظِمَ   the root  3.tth.m  means major, great; it also means bone and the word الْعَظِيمَ is an adjective that by this reasoning means 'that which skeletonizes', therefore, it is meant as an instrument of Resurrection)

لاَ تَمُدَّنَّ عَيْنَيْكَ إِلَى مَا مَتَّعْنَا بِهِ أَزْوَاجًا مِّنْهُمْ
 وَلاَ تَحْزَنْ عَلَيْهِمْ
وَاخْفِضْ جَنَاحَكَ لِلْمُؤْمِنِينَ (15:88

15:88 Do not extend Your sights (eyes, look longingly, envy) to that which We Endowed pairs (couples) of them,
and Do Not Grieve for them.
And lower Your Wings (of Mercy) over/to the Believers.

Sign 15:88 is important to the discussion on catastrophic cusp events in it's allusion to the Prophet (pbuh) 'dipping or lowering His 'wings of Mercy'' like a mother bird would shield her hatchlings by encircling them with her wings. 

But the actual intended imagery has to do with 'folding and bending' space and how to inspect for visual clues in our common everyday experience. 

Here, it draws attention to when looking up at birds flying high overhead they may seem to dip in and out of view (disappear) either due to spherical aberrations in the atmosphere or astigmatism on the part of the observer--or we're all plain giddy to distraction thinking ornithology is a branch of UFOlogy. 

But in a very similar fashion as the astute driver notices such subtle interactions with tay-al-ard or space-fold encounters on the anthropomorphic scale, the phenomenon has equivalence in electromagnetism and light propagation (a compelling argument for the variable speed of light in a vacuum). 

وَقُلْ إِنِّي أَنَا النَّذِيرُ الْمُبِينُ (15:89

15:89 And Say, "Indeed, I Am the Evident (Apparent, Obvious, Conspicuous, Clear) Warner!"(...that's why I keep wondering what happened to my front man?!)

كَمَا أَنزَلْنَا عَلَى المُقْتَسِمِينَ (15:90

15:90 Whom We've Sent to those in disputation (divided, separated, not united)

الَّذِينَ جَعَلُوا الْقُرْآنَ عِضِينَ (15:91

15:91 Those who take the Quran in jest (quibble about, pick over, make biting remarks, take it apart-- idiomatic expression)

فَوَرَبِّكَ لَنَسْأَلَنَّهُمْ أَجْمَعِيْنَ (15:92

15:92 To Your Lord they shall Answer (We Will Question them) Altogether. (Wholey, In the Collective, All of Them Gathered)

عَمَّا كَانُوا يَعْمَلُونَ (15:93

15:93 Of that which (they thought) they were doing.

فَاصْدَعْ بِمَا تُؤْمَرُ وَأَعْرِضْ عَنِ الْمُشْرِكِينَ (15:94

15:94 So proclaim (lit. split, fissure, crack/crevice, rift) that which You are commanded and withdraw from the idolators. (Alternatively, Split/rift/separate by an act of fissuring away (see the driving experience above for similar experience of what it means to 'break away') from that which they command or want of you, and avoid those who join other deities with God, worship other things along with God).

إِنَّا كَفَيْنَاكَ الْمُسْتَهْزِئِينَ (15:95

15:95 Indeed, We spared You from those who mock (blame) you (lit. making a stir, make waves, etc. idiomatic for rabble-rousers).

الَّذِينَ يَجْعَلُونَ مَعَ اللّهِ إِلـهًا آخَرَ فَسَوْفَ يَعْلَمُونَ (15:96

15:96 Those who join with God other gods, they will (come) to know (better).

------------------------------------------------------
Neurotransmission (see gears) means "I love you, but I don't need the same."

Yeah, Right! I think Malcolm is an Old Man, like I go around thinking I am the Queen of the Main!
I just wanted to have everybody change their concept of pre-cursor!

But since it's all been carefully arranged that I can't get off the ground, and I am as of today completely dispossessed, I would like to finally get paid so I can afford to pack my suitcase and move on down the line.

Oh, and I'd really like to see my Late (aka Delinquent) Father right about now.(Thanks for visiting August 5, 2013--let's both try not to be so surprised next time)
----------------------------------------------------

from Tracking Point-Curve Critical Distances, X. Chen, E. Cohen and R. Riesenfeld

The World Turns? Screw That!

Perhaps this post is more appropriately titled , 'An (Hyperb-) Ode to Alan'

"Curvature is the Obstruction to a Flat Field.
Tidal Forces are the Obstruction to an Acceleration Field
Curvature of Space-Time is the same as Tidal Forces."
--From a link associated with "GR02 Gravity Acceleration Equivalence, Gauss’s Law 2008-09-29"

Surah 86 At-Tariq (الطَّارِقِ)
وَالسَّمَاء وَالطَّارِقِ 86:1وَمَا أَدْرَاكَ مَا الطَّارِقُ 86:2النَّجْمُ الثَّاقِبُ 86:3إِن كُلُّ نَفْسٍ لَّمَّا عَلَيْهَا حَافِظٌ 86:4فَلْيَنظُرِ الْإِنسَانُ مِمَّ خُلِقَ 86:5خُلِقَ مِن مَّاء دَافِقٍ 86:6يَخْرُجُ مِن بَيْنِ الصُّلْبِ وَالتَّرَائِبِ 86:7إِنَّهُ عَلَى رَجْعِهِ لَقَادِرٌ 86:8يَوْمَ تُبْلَى السَّرَائِرُ 86:9فَمَا لَهُ مِن قُوَّةٍ وَلَا نَاصِرٍ86:10وَالسَّمَاء ذَاتِ الرَّجْعِ 86:11وَالْأَرْضِ ذَاتِ الصَّدْعِ 86:12إِنَّهُ لَقَوْلٌ فَصْلٌ 86:13وَمَا هُوَ بِالْهَزْلِ 86:14إِنَّهُمْ يَكِيدُونَ كَيْدًا 86:15وَأَكِيدُ كَيْدًا 86:16فَمَهِّلِ الْكَافِرِينَ أَمْهِلْهُمْ رُوَيْدًا 86:17
{Some of 'em want to know what's driving me to do this. Simple vanity! I decided the only way to shed a few pounds around here is to get rid of Gravity.}

The diacritic marks were added to the Quran some time after it was first put down in writing, to ensure the proper pronunciation of the text to avoid any misunderstandings. However, it would appear some people go to great lengths to make sure the meaning is lost on them. So, enough about them.

For the classic Star Trek aficionado who may remember Spock and McCoy facing off in a game of multi-level chess, the Multiple nuances of the Quran are more to do with performing multiple math problems than to dig deep to find a way to screw your neighbor.

For a limited example, take the first line of Chapter 86 At-Tariq. 'The Tariq' has been variously rendered as 'the night visitor', 'the piercing star', 'Sirius', just to mention a few variations on the theme. Tabulated below, in a nod to Multi-level Chess and Math Word Problems, the first line 86:1 consisting of 14 letters is broken down to its basic elements of variables, constants and other arithmetic operators.



If the table on the left, parsing out Sign 86:1 of the Quran, does not make it immediately obvious that one of the relationships embedded in it describes a helical path or orbit, then perhaps some clarification is called for.

I am presuming no one else has stumbled on it since I have never heard anything about this particular information embedded in the Quran, or what turned out to be my very handy-dandy-field-survival-guide, in all the years I've been on this (sad forsaken) planet and considering that this information has been hiding in plain view for over 14 Centuries by our reckoning.

In fact, the majority of those I've encountered over the years only see the worse things in it (which I have always justified as a general lack of literacy in the population) and most of them can only sit around thinking of ways to desecrate it or disparage the One (pbuh) who saw fit to share it with us.

The few more widely read, or the handful following along at apageinthelife, may scoff at the discovery, because there is more vivid imagery and reference to this phenomenon than the example I selected. Not only in the Quran itself, as in Chapter 81 Takwiir (Lit. "Spiralling'/'Twisting,' moving off-center), but in other Ancient lore including the Maya's of South America and the Maori's of New Zealand.

The Maya, of course, are best noted for their 2012 so-called 'doomsday' calendar, and there is a Maori oral tradition that alludes to 'When the Snake Bites the Sun.'

The Snake or Dragon reference appears in one form or another in most world cultures, and while it essentially is a reference to new beginnings from old endings (depicted by the serpent usually eating its own tale), such myths are imparted in simplistic memorable terms akin to presenting someone with a colorful Easter Egg--something that can be easily recalled, so that when we get older and have learned enough or experienced enough, and there comes a time to do away with childish things, we can then truly understand the Reality that 'hatches' from all the fairy tales.

I am probably not as brilliant as the young man looking over my shoulder at our neighborhood Starbucks the other evening, so I can't do multi-level math; and given that I can't even do 10th grade math thanks in great part to those who for whatever reason saw to it I lose the only thing I had going for me (my mind) coupled with the lack of proper care and out-right cover-up from the so-called 'medical community', I have to resort to single-level easy-as-she-goes-so-as-not-to-blow-out-her-one-remaining-brain-cell approach. Since I was never all that great at Set Theory or Statistics, I will go with the Algebra (you can follow along and pick your forte).

The first step, as when working any Code, is to find a Key, or agree on a Convention. Since the 'bismillah' is among the most often repeated phrases on Earth, maybe it is a Key to untangling the Arithmetic embedded in the Quran?





Like with everything else, one must Consider the Source before committing anything to a Methodology. While for convenience I use islamicity.com for an on-line Quran source, I know that the Allah is generally more detailed than what is shown in Sign 1:1 above, so I used wikipedia to get a more faithful representation of the Name 'Allah'.
As shown, Allah comprises an 'alif wasl' which is actually not an 'A' at all but what is called a 'hamza' and since this one appears at the beginning of the word with no prior letter it is pronounced as "Ah" and is called a 'hamza wasl'. Literally, 'hamza wasl' means 'connecting link'.
This is followed by the first L (the Arabic Lam) which in Arabic math notation is used for !factorial but is also the notation for complex numbers of the form r*e^(it). And it connects to the medial L in the Word Allah.
The Medial L (connects two letters, the leading Lam and the Ha (Arabic H that follows). What is noteworthy about this second lam is that it has both the 'shadeh' and the 'dagger aleph' harakat or diacritical marks above it. So, while the first Lam is understood to be connected with the hamza, making the word 'al' as in the definitive article 'the', there is no ignoring what we are to think of this medial Lam.
The 'aliph dagger' خنجر is used to mark or highlight the letter it is over, much like a sign (†) that is used as a reference mark, especially to a footnote (oh, A Clue!). And then we have the 'shadeh' as mentioned throughout the table above meaning, to 'stress' 'double' or 'take root' as well as things having to do with germination and the 'kernel'. And it is worth mentioning that the word 'Aliph' itself means 'compile'.
That the medial Lam is followed by the Ha (ه ), and there is no mistaking that in Arabithmatic ه stands for Euler's number, E, (or, e as in ln(e)=1---like e=2.7182...that E!) may be pointing to Lam as shorthand for complex numbers rather than Permutation, but that's just a guess on my part. (Plenty of room here for puns about 'Mary had a little lamb' and 'Abraham sacrificing a Lamb' or Ram...blah, blah, but let's try to focus).
Euler's number appears often in math and the sciences, and is associated with a range of things from expressing growth (or decay) rates, to Gaussian fields, to simplifying Calculus (like when integrating the Taylor equations).
So, we look for the Truth of the Thing by stringing along the letters. Lam complex form taken once and transcribed to equivalent English is re^(it).

There are two ways to double this; either one should work, so I tried both 2re^(it) and (re^(it))^2. And according to Anyone Who Has Ever Told The Truth of The Matter, There is Only 1 Allah. So, to test the Key, We Trust That ALLAH=1. And thank Heaven for WolframAlpha.com, I was able to generate the table for each case.
The fact that each case based on this Method did not yield a 'False' statement, and that each case had roots and yielded recognizable functions, does seem to confirm that 'Allah-hu-Ahhad' ('God Is One'). (I have to insist it ain't me or any one of you, but I think We may have Met on my worse day on that 'flippin' planet'!). It is interesting to note that each curve varies in the same way given that they all have the same derivatives.

Euler's number also appears when expressing curves in polar coordinates (r,t) and is analogous to expressing a complex number.

A logarithmic, or growth spiral which often appears in nature (spiral galaxies, a hawk' s path toward its prey, the nautilus shell, or a moth' s approach to a flame) when expressed in polar coordinates (r,t) is given by:

r=ae^(bt)
where a & b are Real numbers

Parametrically, the curve is given by:

x=cos⁡〖(bt)〗
y=sin⁡(bt)

A 3-D spiral, or Helix, is formed when a planar spiral is pulled along a third axis, z;

z=t; 0≤t ≤2π

The Helix is not the only type of spiral found in nature, others include the 'Whorl' and the 'Vortex.' All this means is that the World 'Screwing Around' is nothing new, since not only does the Earth Orbit the Sun along the Ecliptic Plane, but it is following the Sun as it hurtles through space on its way to toward the Solar Apex-what is, essentially, a Helical orbit.

The image below is taken from the book Helical Helix : Solar System a Dynamic Process byDr. Pallathadka Keshava Bhat (comments added).



As of 2010 the concept that the entire Solar System moves in a vortex trajectory like a snake moving in 3 dimensions (the 'Solar Snake') instead of a flat plane is not the way it is being taught in our schools. (In fact, in some schools they are still arguing Creationism v Evolution, as if this is even an argument).
As the "Solar Snake" moves either above or below the Galactic Ecliptic (about 26,000 years), it produces the illusion of the 'precession of the equinoxes' or what is described as a wobble in the Earth's polar axis. (At least this is how it appears from the 'Accessible' perspective of Earth's inhabitants, or 'Lower Dimension', than when viewed from outside the Solar System, or the 'Remote' viewpoint from a 'Higher Dimension').
The 'Solar Snake' is creating the so-called wobble due to it's vortical trajectory above and below the Galactic Ecliptic. The Ancients, including but not limited to the Maya, Inca, Egyptians, Indians, Indonesians and Native Americans, knew this and represented the Solar Force as Serpents or twin opposing serpents (twin opposing vortices).

The precession of Earth's axis explanation by way of this 'higher dimensional' viewpoint has interesting ramifications when extending this 'as above, so below' observation to the way information propagates throughout the Creation.
One example is in the similarity between the shape traced by solar system's helical path on the Galactic level compared to sperm on the microscopic level and genetic material (DNA) itself at the atomic level. (I know, this all gives new meaning to the notion of 'panspermia').

And while the examples of the snapshot of the helical solar system, the movement of sperm flagellum and the structure of the DNA molecule are physical 'turns' like that of a screw, this type of displacement is strongly reminiscent of elelctro-magnetic wave propagation.
This 'Reverberating Pattern' transmitted across not only in magnitude (from the Galactic to the Microscopic) but also across forms of Matter and Energy (Movement) cannot be ignored; it is very much like the self-similarity seen in Fractals! The very fact that this self-similarity exists so widely in the Universe must have meaning of 'Grave' (-ity) importance! (Did I scare you?--to know You're Mom died?---You'll be okay, because it's still not as bad as your driving scares me! So, remember to drive safely...(well-timed, aptly-titled JumpStart comics appeared 01.03.2011 in the LATimes; is the 'grammar nazi' comment a personal attack? comics.com)
The Helix also presents as a screw dislocation as it propagates in crystal growth. Screw dislocations are an important mechanism in crystal growth and appear as distinct spirals under high magnification. Turns out, where there is a surface “step” the atoms can more easily add to the crystal, and the surface step associated with the screw dislocation is never destroyed no matter how many atoms are added to it. (The arithmetic description of a ‘step’ is a ‘jump point’ or a ‘discontinuity’ caused by a function being ‘undefined’ at that point, like ‘divide by 0’)
Keeping all this in mind, about how matter holistically travels or imprints these helical paths, an electromagnetic vortex may have something more to add to our understanding of the phenomenon and, in turn, add to our understanding of the Gravity 'paradox' when formulating the Theory of Everything.
An optical vortex is created when light (a form of electromagnetic radiation) travels in the z direction with a phase front in the shape of a spiral. The intensity vanishes at the center (anyone think this is familiar to Gravity at the Center of the Earth where counter forces cancel each other out?) of the optical vortex where the phase is “undefined”.

The image of just such an optical vortex is
taken from a paper by Dr. Ulrich T Schwarz Research Group, Regensburg University. According to that paper;
“…’the threads of darkness’ are the optical analogue to screw dislocations in condensed matter physics. They are defined as topological entities and thus stable. A perturbation of the beam will shift the position of the vortex, but not destroy it (as it is impossible to smoothly merge a spiral staircase).”{…And I suppose this is where I am not to let my anger show and only wonder, ‘Why can’t God Imagine better people?!’} Ok, Enough with the EMO stuff.

Moving right along, we take a second look at where we started:
وَالسَّمَاء وَالطَّارِقِ 86:1
86:1 By the Sky (Heavens) and the Tar(i)q(i)
Which is not to say we are right back where we started because all this has happened in the meantime, so it's not exactly the exact same beginning although it looks strangely familiar (Déjà vu, anyone?--Oh, the French, we'll get to them later...).
The reason the word Tariq has so many associations is probably because when it was first introduced into the Arabic vernacular people thought it quite foreign and they tried to make sense of it through context of what followed, which seems to be about the Sky and the Stars. But the words for Stars and Revelation are homonyms, so 86:3 may be just as likely talking about a Piercing Star as it is a Groundbreaking Revelation. Which brings us to the French.
French is a Romance language and derives from the ancient Latin. It is also known as one of the group of "oïl languages" which share the common word oïl (oui) for yes.
{This is where I have to digress and relate a story about a traveller who shared a (conventional) flight with me and was seated next to me on a business trip some time in the long distant past. As we were flying over New Mexico he became quite chatty about how beautiful it looked from the air and he said that travelling widely for his work had taught him to appreciate all kinds of beauty that is not so apparent to the rest of us just walking around because of the special vantage he had when hearing people speak. He was a Linguist and his work required that he find ways to preserve human language and discover how it evolved, which gave him a wider lexicon than the rest of us and an entirely different way of understanding the World.}
Consider the word الطَّارِقِ (at-tariq) first introduced in 86:1 and then followed by the rhetorical question:
86:2 "And How Would You Know (Who Taught You, or, How Can You Be Able to get the Concept of ) what is the Tariq?"
To someone like my travel buddy, sometime in the '80's, it was probably a no-brainer; but to the rest of us, (or me anyway), it's not incredibly obvious. The nearest Arabic word to it would be طرق "method(s)" similar words mean 'through' or 'way' and secondary meanings are 'knocking, beating, pounding, enter, etc.' It is interesting that an alternative word for 'methods' is الأساليب "al-asaleeb" which sounds a great deal like "the Crosses" ( الصليب the Cross, Crucifixion).
A great many of us know about the story of Jesus and the Resurrection and associate His time on 'the Cross' as a time of 'Persecution' or great 'Torture'. So, we would not be surprised to find that the Latin word torquere, ('to torment'), can remind some of us of the word 'Torque', ('to twist'). And we find even more associations to the Jesus story in similar Latin words like 'Torques", (meaning; 'a chain of,' 'collar,' 'yoke', 'garland', 'necklace', 'gorget', 'chain') and the closely associated 'Torquis' (meaning; 'twisted necklace').
All this is made more interesting when we find that the word 'tarch' or 'arch' is 'Ark' in French, and sounds like 'tark' in Estonian for 'wise, astute, sapient, intelligent...' Which brings us around full circle to the word in Farsi (Persian) for torque, where it's taken directly from the contemporary word and its modern-day meaning; 'torque' transcribed in the Arabic/Persian alphabet as 'تورک' (tork), which looks and sounds a lot like the definitive طَّارِقِ (allowing for variations due to trascription from one laguage to another).
The Answer to the rhetorical Question posed in 86:2 (although none is needed) is:
"Certainly Not Google language tools!"
Since a recent translation of 86:2 using Google Language Tools yielded the following interpretation:
"Everybody Knows What Tariq (86:2)" (is).
{I would be convinced otherwise if every government agency had not at one time or another visited this site, even by way of Malaysia and Siberia, ok? I know yousguys tamper with it, because I would not expect those visitors' default language to be English.}
Essentially, this is what it is:
86:3 An-najm al-thaqib86:3 The Piercing Star; A Penetrating/Acute/Sagacious Revelation (acute/keen/boring (like with a hand-drill/perforator Insight/Awakening)
86:4 Inna Kulla Nafsitin llamma 3aliha hhafizhu86:4 Indeed (Truly) Every Being (Soul) Has Overseeing it (Over It) A Saviour (Keeper, Guardian, Protector, Watcher)
86:5 Fayuntthiri al-insannu mimma khulliq86:5 So let (such that) the Human Being See (Understands) Of What (they) Are Created
86:6 Khuliqin min ma'in daffiqin86:6 Created From/Of Watery Effluent (stream, race, influx, afflux, outpouring, inflow/outflow, pouring, pumping, effluence...)
86:7 Yakhruju min bayina al-ssalbi wa al-ttara'ibi86:7 Coming out (emerging, exiting, surfacing) from/of between the 'al-ssalbi' (n.; steel, Crux, crucifixion, loin, ramrod, cross-cut, betterment. v.; crucify, harden, consolidate, stiffen, temper, call out, sear, castigate. adj.; solid, firm, rigid, tough, stiff, concrete, robust, metallic, adamant, unyielding, inflexible, unkind, stark, horny, stubborn, tenacious, resistant, solidity, cruel, corneous, persistent, callous, stabile, out-and-out) and 'al-'ttaraa'ibi' (Alterae (Altair); var. رأب ra'b, bridge, garage; al-tara ibi (ForeFathers' + White Flyers).

The Northern Cross, or Cygnus (The Swan)__Backbone of the Milky Way

On one level 86:6 and 86:7 may very well be a lesson in biology and procreation, but the text is troubling when we have to try and figure out what the exact body part the 'effluent' or 'flood, stream' is emerging from between given that the words 'al-ssalbi' and 'al-ttara'ibi' don't, as far as I can find, correspond to any widely accepted body parts as such. They have been variously interpreted to mean the ribs, loins, or rib cage and the pelvic arch, but this seems contrived.
So, for now, we have to look elsewhere in our Universe to make a more Immediate Connection.
The Galactic Plane (Equator) runs right through the Northern Cross (Cygus, The Swan) where the asterism Fixed by Deneb and Albiero forms the long ‘Staff’ of The Cross; and Delta Cygni, Sadr, and Gibeah form its outstretched 'arms' (cross-bars).
Sighting the Northern Cross is the same as looking directly into the Milky Way disk since it floats like a backbone of the Milky Way – the luminous River of Stars passing through the Northern Cross and stretching across the sky. On clear, dark Winter nights this “milky” swath of sky appears as a hazy band and is really an edgewise view of the Galactic Disk.
The "Summer Triangle" likewise fixes the orientation of the Milky Way Galaxy as it flows out through one of the 'legs' formed by Vega and Altair, with Deneb at its western Apex.
Each of these stars in the Northern Cross and the Summer Triangle are associated with avian Constellations: Deneb and Albiero and Delta Cygni mark the Tail, Beak, and Wing of The Swan, respectively; Gieneh, means 'wing' in Arabic and it represents a wing of Corvus, the Crow/Raven (Gamma Corvi), and the eastern outstretched 'wing' of Cygnus the Swan (Epsilon Cygni); Vega is the brightest star in Lyra associated with the mythic Eagle/Vulture that swoops between Heaven and Earth; and Altair is a main star in the Aquila and derives its name from al-nasr-al-ta'er, 'The Flying Eagle', of legend; and finally, Sadr at the center of the crossbar in the Northern Cross is from the 'Breast' of the Hen.
So, while anatomically we may yet have a few more things to learn about human physiology, it would seem what we know about the Cosmos provides a more fitting depiction of what Signs 86:6 and 86:7 are on about. Since it would seem to indicate that the flow of the Milky Way through these fixed points has something to do with Birth or Resurrection. A Birth that our Ancient Forefathers noticed on a Galactic Time Scale in its streaming through what is alluded to as a 'bridge' associated with these 'White Flyers'. It's not surprising that Deneb, Vega and Altair are all white Class A stars related to Birds.
A 'bridge' connects or links places and it also enables communication (a span across a physical barrier or Time) and the secondary meaning of the word رأب ra'b being 'garage' may lead to the inference that the destination is a place for rest and repair, whether it be for cars, stars, UFOs, or people.
86:8 Innahu 3alla raj3ihi laqadirun
86:8 (Indeed) He Is Able (Has Power Over, Can Cause) him (the Human) to Return (Revert, Come Back, Repeat, Reinstate, Snap back, pass back, reestablish, send back, report back, resound) (aside, is that like a threat?)
86:9 Yawma tubla assara'iru
86:9 On A Day Secrets Are Displayed (laid bare, put forth, the understanding is that they are 'worn out' for all to see, like clothing, with all connotations including 'bearing them' and their being 'erased' and/or 'worn down' in that there will be no way to make excuses for them)
86:10 Fammaluhu min quwatin wala nassirin
86:10 He will have no other Helper/Power/Force or Friend/Patron/Benefactor
86:11 Wa al.sama' tthati alraj3i
86:11 And the Sky (Heaven) Relates the Feedback
86:12 Wa al.ardi tthati alssud3i
86:12 And the Earth Relates the Rift/Flaw/Fissure/Crack/Separation/Segregation...
86:13 Innahu laqawln fasln
86:13 (Indeed) He Can Say (Utter, Call, View, Determine) the Decision (separation season segregation division disconnection isolation severance seclusion demarcation disjunction parting dissociation breakthrough displacement; v., separate disconnect detach break dismiss fire segregate remove adjudicate cut isolate determine decide settle cut off detail sever resolve divide disentangle dissociate sack discharge judge partition lay off set apart expel part itemize wean displace adjudge dissociate oneself from disunite disjoin arrive at a resolution cashier
render a judgment particularize elaborate seclude make a decision sunder have a final word)
86:14 Wammahua b'al hazli
86:14 And He Is Not Kidding (not joking); He Is Serious
86:15 Anahum yakeydoo'na kaeidana
86:15 They are scheming a plot (They plot a plot; plan an artifice, machination, scheme, trick)
86:16 Wa'akeydo kaeidana
86:16 And I Plot a Plot...
86:17 Famahali al.kafireen amhalhum ru'wayidana
86:17 Allow Time for the Disbelievers (Unfaithful)--Take It Easy On Them (Deal Gently with them, Allow (them) Time for A Reprieve).
...I can't believe You; they have the supercomputers, a nuclear arsenal, all the national labs, and their sanity & You Tell me to take it easy on them?! Fine. Here, I Plot a Plot!



PS Henry, I was kind o'hope'n you took off with the quantitative maths while I perigrinated the qualitative aspects. The Chapter:Verse may be the actual parameters for the steps. For example, Sign(1:1) would indicate use variables=1 and result=1 ; and test for True. The example given for الله above yields:
; ; ...
True; True; True...

Coma Therapy

Sleep that knits up the ravell'd sleeve of care...
William Shakespeare

Has anyone tried Coma therapy for Jani?--a 6 year old schizophrenic with psychosis so severe that massive doses of '(antipsychotic) medications seem to skip over her'.
If you can't part with her for a while try it in three-day increments.

Her Cats and Rats are probably how this 6 year old is communicating that she is having difficulty reconciling her high intelligence with her sensual (sense-u-all) side. It would be unkind to continue with adult medications that are probably doing more harm than good and certainly stay away from stuff like electro-shock therapy, that would be just plain cruel and stupid.

And we all know that you can't fix stupid.

If her psychosis is as severe as described in the Los Angeles Times article Jani's At The Mercy Of Her Mind, her 'brain' is probably racing along faster than the speed of light and can only stand to benefit from a restful induced sleep and welcome holiday from the drug interactions that are probably ravaging her developing mind.

PS Suggested reading for Jani when she 'wakes up,' Keneth Grahame's The Wind in the Willows.

Note: The LA Times Article http://www.latimes.com/features/health/la-he-schizophrenia29-2009jun29,0,4834892.story

Phunny Physics

E=m(c* π/3)^2

The Earth is not exactly round, that's why it's bipolar

Check out The Lady of the Lake

http://www.polarbearandco.com/paulduhoux/essays.htm

In 2001, researchers from the Two Degree Field (2dF) Study (Australia) and the Sloan Digital Sky Survey (Arizona, USA), reported that the universe makes a sound (attenuated and faint at this point in time). While this may be counterintuitive (sound travels in a vacuum?), in the nascent universe I think the sound was not unlike the sound a genuine Tibetan singing bowl makes.

Along with this finding, the study also confirmed that the universe is composed of just 4 percent regular matter (stuff; ie., people, stars, dust), 25 percent dark matter (mystifying stuff that acts like it’s there but we can’t see; ie., jinns), and the remainder dark energy (baffling stuff like the force that is driving the universe to expand at an increasing rate; ie., ‘We’).

وَالْجَآنَّ خَلَقْنَاهُ مِن قَبْلُ مِن نَّارِ السَّمُومِ
Al Hijr 15:27

And We created the jinns before (humans) from a toxic (scorching) fire.

وَخَلَقَ الْجَانَّ مِن مَّارِجٍ مِّن نَّارٍ

Al Rahman 55:15

And We created the jinns from a smokeless fire.

وَالسَّمَاء بَنَيْنَاهَا بِأَيْدٍ وَإِنَّا لَمُوسِعُونَ
Zariyat 51:47

And We built the sky (Universe) by our hands (favor/endorsement) and We are expanding it.

Mystical Math

I hope someone can check the math:

U = N cos^3 theta + E ( sin cos ^2 theta) - D sin theta

V = N ( -cos^2 sin theta sin phi - sin cos^2phi) + E (-sin cos sin phi sin phi + cos^3 phi) + D cos theta sin phi

W= N (-cos^2 sin theta cos phi - sin cos sin phi) + E (-sin cos sin phi cos phi-cos^2 sin phi) + Dcos theta cos phi

Or for those of us still steering by the sun, is the rotational matrix:

[cos(phi)*cos(th)*cot(psi)-sin(phi)*sin(psi) -sin(phi)*cos(th)*cot(psi)-cos(phi)*sin(psi) sin(th)*cot(psi)]
[sin(phi)*cot(psi)+cos(phi)*cos(th)*sin(psi) -sin(phi)*cos(th)*sin(psi)+cos(phi)*cot(psi) sin(th)*sin(psi) ]
[-cos(phi)*sin(th) sin(th)*sin(phi) cos(th) ]