Showing posts with label Perception. Show all posts
Showing posts with label Perception. Show all posts


A Point Of You

Surah 94 Ash.Sharh (The Splitting, Slicing, Opening Up...)
أَلَمْ نَشْرَحْ لَكَ صَدْرَكَ (94:1
وَوَضَعْنَا عَنكَ وِزْرَكَ (94:2
الَّذِي أَنقَضَ ظَهْرَكَ (94:3
وَرَفَعْنَا لَكَ ذِكْرَكَ (94:4
فَإِنَّ مَعَ الْعُسْرِ يُسْرًا (94:5
إِنَّ مَعَ الْعُسْرِ يُسْرًا (94:6
فَإِذَا فَرَغْتَ فَانصَبْ (94:7
وَإِلَى رَبِّكَ فَارْغَبْ (94:8

94:1) Did We not Expound upon your feelings/perceptions (literally, Had We Not Opened Up Your Breast/Chest)
94:2) And removed your burden
94:3) That weighed heavily on your back
94:4) And amplified your remembrance
94:5) For with every hardship comes ease
94:6)  Indeed, with every hardship comes ease
94:7) So, once you are free (of burdens), remain steadfast
94:8) And turn your attention to your Lord's Desires

What else could have prompted the long drive? Did you get lost on the green?

34.05116, -118.419851 bene NNE (I mistook for ENE)
34.047836, -118.430409 selby N
34.040244, -118.463253 santa monica NNE (I mistook for ENE)

The problem is what could cause such an error?

A question for a mavin in the field of applied mathematics (as if there is such a thing).

Shamrock (3-leaf clover)
Trefoil knot 3-1 (arithmetic), Tri-star (wheel arrangement)

Alhambra Motif, Rosette (4-leaf Clover)
Knot  , Romanesque Cross


Unfolding, Inversion, Rewrapping

5-Point Star, Cinquefoil Knot (Prime Knot D_5, or 5_1),
Solomon's Seal Knot (Link)

Star of David, Abraham's Shield,
The Secret I'm In

Surah 4 An.Nissa (Women)
الَّذِينَ يَتَرَبَّصُونَ بِكُمْ فَإِن كَانَ لَكُمْ فَتْحٌ مِّنَ اللّهِ
قَالُواْ أَلَمْ نَكُن مَّعَكُمْ وَإِن كَانَ لِلْكَافِرِينَ نَصِيبٌ قَالُواْ أَلَمْ نَسْتَحْوِذْ عَلَيْكُمْ
وَنَمْنَعْكُم مِّنَ الْمُؤْمِنِينَ فَاللّهُ يَحْكُمُ بَيْنَكُمْ يَوْمَ الْقِيَامَةِ
  وَلَن يَجْعَلَ اللّهُ لِلْكَافِرِينَ عَلَى الْمُؤْمِنِينَ سَبِيلاً (4:141
4:141  ....And never does Allah (God) allow the unfaithful an advantage (a pathway, course, track) over the Believers (God's Followers), (i.e., God never allows the unfaithful to do any harm to the faithful...)
Pearls Before Swine
June 13, 2013
Origami as Crumbled Paper Ball

Pearls Before Swine
June 14, 2013
Origami Salami Tsunami

How's that for Top Secret--Ayeh 4:141 (Quranic Verse 4:141) was posted in the interest to allay any fears that this information can be  put to any viable use by those it is not intended for, and the fact that I am growing weary (wary, leary,  whatever means perturbed and tired of following'em around the www) of some pages and posts found at A Page In The Life being redirected to porn sites.

..when the Sun moves off-center (Taqwir)

Refer to The World Screwing Around
And Surah 81 Taqwir
How The Sun and Planets Really Travel, Interesting Visual Here (
Note: Earth 1 in the previous orbit around the Sun, prior to translating helically along with the Sun to Earth 2 position

The Sun at that point would appear to have moved Off-Center just as described in Surah 81Taqwir.

The second Focal point F2 is actually very faint and when drawn to scale is not that far off from the Center of Mass of the Sun (the distance is usually exaggerated for illustrative purposes), and may not be in the planar elliptical orbit at all, as sometimes rendered.

Comments are welcome, only if they are relevant to this premise.

{As an aside: 
Surah 6 Al.An3'am (Cattle, Chattle)
وَكَذَلِكَ جَعَلْنَا لِكُلِّ نِبِيٍّ عَدُوًّا شَيَاطِينَ الإِنسِ وَالْجِنِّ
 يُوحِي بَعْضُهُمْ إِلَى بَعْضٍ زُخْرُفَ الْقَوْلِ غُرُورًا
 وَلَوْ شَاء رَبُّكَ مَا فَعَلُوهُ فَذَرْهُمْ وَمَا يَفْتَرُونَ  (6:112  
6:112) And in this manner We Created for every messenger enemies, demons from humans and jinn (invisible forces); they awaken/stir each other amongst each other with fetching sayings meant to tempt. Had Your Sustainer Willed it otherwise He would not have done this, so ignore them and all their false devising (imagery).

You know, SteveH, I think you should stop with the microwave audible effects

So what if you are a self-professed asshole  (this joke has run its course), and you are very wealthy and have nothing better to do except to equip yourself and your valiant Starbucks computer bandits with headphones and this stale harassment technique. 

The fact is neither you nor they are adding anything joyful or beneficial to my life and after last Sunday's abusive treatment at the hands of your cohorts in an Emergency Room setting, I think you should just leave me alone (and return my belongings (including my iPhone) that you had them take from me under duress--and thanks for playing my iTunes at Starbucks Cross Creek Road). 

You have a very beautiful life and a beautiful wife and 3 strapping young lads to call your own--so leave me alone and stop disturbing the Peace.  

And if I ever hear You or anyone refer to me as your 13th wife, that means that You, Ya-Sulaieman, have broken a promise to me, like when did that ever happen? {And here's what Your one wife had to say about it--'You've had 1 too many, don't come back without that one!'}

But evidenced by the massive deployment of Your forces, either You cannot get them under control or the more likely explanation is that You are thinning out the field.

Surah 27 An.Naml (The Ants)
وَحُشِرَ لِسُلَيْمَانَ جُنُودُهُ مِنَ الْجِنِّ وَالْإِنسِ وَالطَّيْرِ فَهُمْ يُوزَعُونَ (27:17 
27:17) And gathered onto Solomon His forces of Jinn and Humanity and that which flies (Al.tayiri) and they were arrayed in order (battle order, ranks). (See Surah 37)

Surah 34 Saba' (Sheebah)
وَلِسُلَيْمَانَ الرِّيحَ غُدُوُّهَا شَهْرٌ وَرَوَاحُهَا شَهْرٌ
 وَأَسَلْنَا لَهُ عَيْنَ الْقِطْرِ
وَمِنَ الْجِنِّ مَن يَعْمَلُ بَيْنَ يَدَيْهِ بِإِذْنِ رَبِّهِ
وَمَن يَزِغْ مِنْهُمْ عَنْ أَمْرِنَا نُذِقْهُ مِنْ عَذَابِ السَّعِيرِ (34:12
34:12 And Solomon's Command of the Winds; their course coming on the morrow one month (journey) and going one month (journey); and We Bestowed upon Him 'determining rainstorms'  (var., 'the eye of the storm,' 'how to gauge distance/diameter,' 'a fount of molten copper,' 'percolating wells, i.e, underground wells, oil, natural gas, water, mineral baths, etc.');
And to know the workings of the Jinn by His Lord's Leave;
And whoever amongst them deviates from Our Command, tastes of an austere punishment.

 فَلَمَّا قَضَيْنَا عَلَيْهِ الْمَوْتَ 
مَا دَلَّهُمْ عَلَى مَوْتِهِ إِلَّا دَابَّةُ الْأَرْضِ
 تَأْكُلُ مِنسَأَتَهُ
 فَلَمَّا خَرَّ تَبَيَّنَتِ الْجِنُّ أَن لَّوْ كَانُوا يَعْلَمُونَ الْغَيْبَ
 مَا لَبِثُوا فِي الْعَذَابِ الْمُهِينِ (34:14 
34:14) Once We Ordained death to Him (Solomon's death as a mortal),
Nothing indicated His death except dabatun (crawling creature, maybe a worm, or other beast) from the Earth that gnawed through His staff (He leaned on while seated),
And once He fell (from the chair as He leaned on His compromised staff) His death became apparent to the Jinn, had they known the Unseen/Invisible/Hidden Reality,
They would not have continued to toil in demeaning work.

Surah 41 Fussilat (Distinction, Clear Explanation)
وَقَيَّضْنَا لَهُمْ قُرَنَاء فَزَيَّنُوا لَهُم مَّا بَيْنَ أَيْدِيهِمْ وَمَا خَلْفَهُمْ
 وَحَقَّ عَلَيْهِمُ الْقَوْلُ فِي أُمَمٍ قَدْ خَلَتْ مِن قَبْلِهِم مِّنَ الْجِنِّ وَالْإِنسِ
 إِنَّهُمْ كَانُوا خَاسِرِينَ (41:25
41:25) And We Ordained to each of them (the faithless) their dual that made fair seeming to them whatever they were doing and their past deeds, and Our Promise came True throughout the Nations that had passed before them of the Jinn and Humans; indeed, they were the losers.

Ballard Street Comic Panel
"Ok. Ok. You know how to drive."
May 27, 2013
Just because my men are quiet around here doesn't mean they are inactive, in fact, we aim to fight to the last man--seeing how we are already dead, anyway, it can only get better for us.

The fact is that I am not the Queen of Sheba, and I am not a Messenger, and whatever I have been going through and continue to experience feels a lot like abuse from your collective selves, and I am simply not up for, I will continue to not accept any outcome where I don't come up the winner--apparently I had to earn my keep even while it seemed to the untrained eye that I labored for no immediate recompense--they actually even pitied me with their sidelong glances (apparently they hadn't seen me drive this town). 

Imagine that! And still try not to come up out of your graves laughing!

And, Ya-Suleiman, don't call after me,  'Peace!', like You are calling Your dog to come home--my Father will remind You, that particular Star always rises over (and no, she can't be monetized or made famous or do a cover for Esquire, that's why she wonders what is up with her 'husband' and why he isn't taking care of the 'business' end). 

...And, Yes! That's exactly what the Ka'3beh is for! (That's an answer to a direct question, not a non sequitur.)

The Ka'3bah is central to the Hajj, where pilgrims perform either the formal Pilgrimage (Hajj) or make lesser visits off-season, an Umra, and circumambulating the structure is a major part of performing this rite.

And it was never the case, historically speaking, that anyone was ever kept from visiting Mecca and performing either the Hajj or the Umra if they were able to do it.

So, preventing anyone based on religion, race, creed, or sexual persuasion from performing this rite is highly suspect as very poor judgment and only bolsters my worst suspicion that I keep waking up on the wrong planet.

Here, I must finds the textual reference to support such a position (Sign 3:96 and 3:97), given that even my life-long friends think I had such suffering as visited on me well-deserved for my take on expiating the Quran:

Surah 3 Al'3mran 
(Jeez isUs! Family--That should stop the speculation how He went from '3esau to Jesus--how's that for the Brooklyn angle and being married to the Mob?)
3:96 إِنَّ أَوَّلَ بَيْتٍ وُضِعَ لِلنَّاسِ لَلَّذِي بِبَكَّةَ مُبَارَكًا وَهُدًى لِّلْعَالَمِينَ 
3:96 Indeed, the First Temple established (situated, affixed, connotes it was 'designed/outlined', possibly architecturally speaking) was that at Bakka (clearly this refers to the Kaaba in present day Mecca); a blessing and a guidance for all the worlds (humanity, mankind, and all of creation's creatures/communities)

3:97   فِيهِ آيَاتٌ بَيِّـنَاتٌ 

مَّقَامُ إِبْرَاهِيمَ 
وَمَن دَخَلَهُ كَانَ آمِنًا 
وَلِلّهِ عَلَى النَّاسِ حِجُّ الْبَيْتِ 
مَنِ اسْتَطَاعَ إِلَيْهِ سَبِيلاً 
وَمَن كَفَرَ فَإِنَّ الله غَنِيٌّ عَنِ الْعَالَمِينَ 
3:97 In it (The First Temple) are Clear Signs (Messages);
Ibrahim's Station,
and whoever enters it is Safe (Secure, At Peace).
And God Established the Pilgrimage for people (Nas, communities) to it;
Whoever is able to make their way to it (سَبِيلاً  sabil==travel, setting a course, etc.),
And whoever belies/blasphemes (this), truly God is Needless of the Worlds! (ie., God is not in need of His/Her/Its Own Creation and is Independent of it. Compare Sign 3:97 to John 5:41 where he writes to "I do not accept/need/want honor from humans...")

According to Signs 3:96 and 3:97, not only is visiting the Kaaba (Hajj) intended for all of creation, but it is incumbent on anyone able to make the pilgrimage. And such an undertaking is not for God's benefit, as concluded in Sign 3:97 since God is independent of and not in need of the Creation, but it  serves as a benefit to humanity and anyone or anything else that finds itself within its environs.

But my friends mean well and they are still my friends and I know they love me enough to express such opinions freely, yet they still stop just short of calling me crazy--yeah, where's the fun in that!

Besides, what is up with these Arabs that call this Kaaba, this Projected Protracted Solid Structure, A Cube? And according to Sign 3:96, it may have actually been planned that way and not just built ad hoc.

None of the sides measure the same!

A planet where Arabs don't know math or understand geometry?

Or, perhaps they already know the orientation of the projective plane from the aerial view that makes it look like the Cube it is named for on the approach.

Let's have a look, shall we?

Surah 55 Ar.Rahman (The Merciful, var. The One Who Embeds Into the Wombs)

يَا مَعْشَرَ الْجِنِّ وَالْإِنسِ
إِنِ اسْتَطَعْتُمْ أَن تَنفُذُوا مِنْ أَقْطَارِ السَّمَاوَاتِ وَالْأَرْضِ
فَانفُذُوا لَا تَنفُذُونَ إِلَّا بِسُلْطَانٍ (55:33  
55:33) O, company of Jinn and Humanity,
should you intend to proceed/permeate/penetrate beyond the regions/diameters of the Skies and the Earth, then pierce them; 
you cannot do so without Sanction (God's Authorization)!

See 2:127 'facing'/entry/sanction

The Kaaba with Various Stations Numbered (Abraham's Station shown as Number 7)
The Green Line indicates the beginning of the Towaf (circumambulating) at the East Corner  in a Counter-Clockwise Direction Around the Kaaba 7 times; the first 3 rounds at a fast pace and the rest at an ordinary pace. 
The Kaaba And Hatim
Dimensional Drawing
The Corners Align Roughly to the Cardinal Directions:
East Corner (Black Stone) _W Corner (Ash.Shami) Levantine (E-W Minor Axis);
North Corner (Iraqi)_South Corner (Yemeni) (N-S Major Axis).
The South-facing wall aligns with Canopus (alpha_Carina, a bright star in the Keel of the Southern Constellation Argo Navis_ar. Suhail).
West-Facing Wall toward Winter Solstice,
North-Facing Wall toward Summer Solstice.
Cube Top and 2-Point Perspective Views
Foreshortening of Sides.
The Roof of the Kaaba is Flat so it would appear Square from the Aerial View
(despite the difference in Height of  the walls)

Cube, Vanishing Point and Horizon Shown,
2-point Perspective View
Taking this as the foreshortened view of the Ka'3ba, the vertical axis aligns with the East corner where the Black Stone is inlaid, and the overall Height = 13.1 m (43 ft), the side shown with the VP apparent is approximately ~11 m  (36 ft), and the other foreshortened side is about ~ 12.8 m (42 ft).
Image Credit

Triangle UFO
Artist's Conceptual Rendering
Compare with 2- point Perspective of Cube
Let's take the Ka'3bah's height, shown in the 2-point perspective aligned with the vertical axis, as the actual height from the baseline (the ground) of the projected Cube, 13.1 m or 43 feet (the Height may actually be different along each wall, no accurate drawings available); that is to say no apparent foreshortening or elongation.

Then that assumes the true measure of the sides is 13.1 m.

The legend about the original Kaaba is that Adam had built it directly below the one in Heaven. So, calling Heaven the True Situation of the Perfected Kaaba 13.1 x 13.1 x 13.1 m (let's just say), then the one on the 'earth' is essentially the 'projected' corresponding cuboid.

And in order for the Heavenly Kaaba to be the perfect Cube implies that heaven is a hyperdimensional space and the observer, in order to see it as a perfect cube in one glance, is also in a hyperdimensional space.

But it would follow that since the earthly Kaaba is in 3-D, the hyper dimensional original could be 3-D + 1, but also 3D+2, +3 and so on, and that is only limited by our own understanding of what 'heaven' or that higher dimensional realm is.

For all we know, it could be limitless in dimension.

If we assume a Heaven of only +1 spacial dimension higher than home-Earth, we can apply dimensional analogy to understanding the projection of such a higher dimensional cuboid.

A Tesseract Projects as
3-D Volumes in 3-D space
Knowing that a three-dimensional (3-D) object is bounded by two-dimensional surfaces (2-D) and  that a 3-D cube is bounded by 6 square faces, then a four-dimensional (4-D, spacial dimension) cube, the tesseract, may be bounded by three-dimensional volumes. 

Arithmetically, it can be shown that a tesseract is indeed bounded by 8 cubes (its net). It would be interesting to see how this compares to the 2-dimensional Lusona figure with its central 8 diamond elements.

This is key to understanding how to interpret a three-dimensional projection of the tesseract

The boundaries of the tesseract project to volumes in the image, not merely two-dimensional surfaces.

Casting shadows is analogous to projecting solids.

In a 3-D world, 3-dimensional objects cast  2-dimensional shadows; and, by inference, a shadow cast in a 4-D world of a 4-D object is 3-dimensional.
"If the wireframe of a cube is lit from above, the resulting shadow is a square within a square with the corresponding corners connected. Similarly, if the wireframe of a tesseract were lit from “above” (in the fourth direction), its shadow would be that of a three-dimensional cube within another three-dimensional cube. (Note that, technically, the visual representation shown above right is actually a two-dimensional shadow of the three-dimensional shadow of the four-dimensional wireframe figure.)"--wikipedia
Understanding this, it is a simple exercise to establish the viewing angle (plane) and the coordinates of the True structure, and may help us come to grips with the fact that we regularly visit the 'shadow world' throughout our time on home-Earth, while we are blissfully oblivious to the fact of that particular matter.

Here's a guess, about 23 -37 degrees ENE and about 4-8 feet up in the air?

Just kidding, but how close did I get...

2:158 safa and marwa
3:96 first temple
3:97 clear messages//entrance 4:27-29 entry//
5:16 path//5:75 Mariam 'sadiqat'//5:77 re wrong path
5:17 creative power
5:18 dominion
5:19 persistence //52:4 enduring//
5:20 reason prophets rise
5:23 'the gate'
5:66 convergence?
5:97 symbolic
9:19 tending House
17:1 Ascension
(5:13 forgetting & forbearance//5:14//5:15 concealing scripture)

Essentially, this is an exercise in Topology--preservation of the properties of a shape as it undergoes continuous deformation (without tearing or puncture).

Being able to execute a new function, or a latent human ability, cannot be undertaken unless, on some level, its principles are understood to make sense and it can be readily envisioned.

Surah 68 Nun (ن)
ن وَالْقَلَمِ وَمَا يَسْطُرُونَ (68:1
مَا أَنتَ بِنِعْمَةِ رَبِّكَ بِمَجْنُونٍ (68:2
وَإِنَّ لَكَ لَأَجْرًا غَيْرَ مَمْنُونٍ (68:3
وَإِنَّكَ لَعَلى خُلُقٍ عَظِيمٍ (68:4
فَسَتُبْصِرُ وَيُبْصِرُونَ (68:5
بِأَييِّكُمُ الْمَفْتُونُ (68:6

68:1 Nun, By the Pen and What They Write
68:2 You are not, by Your Lord's Grace, Mad
68:3 And, indeed, Your reward is obliged (unfailing)
68:4 And You are bound toward a Sublime Creation
68:5 So watch, and they will see
68:6 Which of you is beguiled

The idea behind Sign 68:2, and it's reassuring the Messenger (pbuh) that He is not mad, occurs frequently in the Quran; apparently this reassurance was of some importance whenever His concept of the Reality He was born (borne) into was challenged to some great effect. Not so in my case, where I have come to embrace my insanity...


WHO Wants To Know

"Who Is This Sinful Woman?"--He Keeps Asking, I think it best to Let Him Know!

 WHO = Sin ∮u l {}=matrix [mass.acceleration.N]

(m means mass, mass flow, or Molar mass;
a means acceleration, Area, or Helmholtz function, specific or total, u-Ts kJ/kg or U-TS kJ; or Ampere.
N means force in Newtons --appropriate if m=mass, a=acceleration; or N number of moles, or N is set of natural numbers; or n is an integer variable, or n is the order of the matrix)}

Giving the inquirer the benefit of the doubt that there is no sinister or malicious intent motivating such a query, we try to make sense of it in a matter accessible to what we are on about here, the Masked Truth in All Its Guises at A Page In The Life, by taking the liberty of interpreting sin.f.ul as:

...the sine of the integral (f taken as a stylized symbol for the integral sign, linear or closed path, since the integral symbol is a modified s for Sigma, or summation, and the f is akin to an inline font for that arithmetic symbol, essentially leading to the same quasi conclusion to take the integral...who exactly invented fuzzy logic?)

...or to make it easier f may simply mean a function of... in this case f(ul)

...u is shorthand for taking the integral by parts so the understanding is to select u st we integrate in terms of du

..and from the arabithmetic: L= lam = z= e^(it); t= time or phase (theta)

If integration is assumed it gives a function along the line:

 sin [(∮(u) z )]

with z= e^(it) the input to looks like:

with the following solutions:

and for t and u, Real:

series expansion at u=0, note the Big O notation:

Integrating by parts and letting u= it or iθ

then du = i dt or i dθ

st the case du/dθ gives us dθ = -i du

To rephrase the question:

WHO is

 [m,a, force (newtons)]

W may mean: the Lambert W-function (aka the Omega function), a simple function with many applications;  the inverse (a reflection about the line y =x) of f(W) = W(e ^W); the Lambert W-Function is related to the tree function , the series T(x)= x + (2/2!) x ^2 + (3^2/3!) x^3 + (4^3/4!) x^4 + (x^5/5!) x^5....which converges for |x| <1 e="" i="">, as T (x) = -W(-x)-- the tree function is useful in deriving the limiting distribution of cycles in random mappings; the series parametric (x^(n-1)/n) with n=0, is log x; or  a throw or wurf as in W-curves which include: conics,  log spirals, powers, logarithms and the helix, but not sine curves. Sinh (x) and cosh (x) are hyperbolic functions that are w-curves, however; or Work (kJ) or Power (kW) or work per unit mass (kJ/kg);

H may mean: Handamard/Schur Product (binary matrix operation A o B (i.e.., the Trace of the matrix product), a submatrix of the Kronecker product); or quaternions or Hamiltonian quaternions {a + b i + c j + d k : a,b,c,d ∈ ℝ}; specific  or total enthalpy u + Pv kJ/kg  (or U + PV kJ); convection heat transfer coefficient (W/m^2 C); or h as Planck's constant 6.626...x10E-34 (m^2 kg/s or Js),  unit of magnetic inductance, the Henry  ;

O may mean: Big O notation, order of asymptotic behavior of a function (strict upper bound infinity or infinitesimal);

the exact solution for which is:
and a series expansion at z= 0:

Plots for the function -i sin Integral of [u e^u du]

To narrow the guess by using unit analysis, start with the dimensionless guess where:

W alludes to the Lambert W-function, z= W(z) e ^(w), for w = any complex number (a + bi):

In this case w=it ; the Real part of the complex number a= 0.

The function  W(z) = W eW, and many expressions involving W(z), can be integrated by substituting: 
w = W(z), i.e. z = w ew .

Taking the log of both sides:  log W(z) = log z - W(z), valid at least for the principal branch W(0) when z >0.

To integrate expressions using the W-function:

Integral of the Lambert W-function derived from earlier work attempting to integrate the Navier-Stokes equations in parametric form; x = pe^p, dy/dx=p.
It was evident that y was the antiderivative of W(x), providing a technique for symbolic integration of W(x), C is a constant of integration.
Integrating problems containing W is really a special case of integrating expressions that contain inverse functions; simply a technique of a special change of variable.

For example,  putting w = W(x), then x = w e^w, and dx = (w + 1) e^w dw, the integral above then becomes:
Integrating expressions containing the W-function is really a special change of variable technique, and is valid for all branches of W, as defined, since (d/dw) we^w 0, at any interior point to the branch.

The technique as described above is mentioned in a paper by Corless, Gonnet, et al, On the Lambert Function (Department of Applied Mathematics, University of Western Ontario), as having led several authors to rediscovering:

Essentially, a statement pertaining to elementary functions, which follows from  Liousville's Principle. Simply stated:

 such that:  

This has applications in the computer sciences in that it allows the Risch algorithm to be applied in order to determine whether or not integrals containing the Lambert W-function are elementary functions.


For our purposes here, integrating the W-function, where u= it:

...and from His sin.f.ul assesment of Her, we already have u eu on the r.h.s of the rebuttal.

W-function_h_o is either:

sin (x), where x = f(ul) , x some function of (ul), i.e..,  ue^u=it(e^(it)), st sin (x) is:

sin (x) where x is some function f(ul) or f(it e^( it))

or f(ul)= integral of it(e^(it))  st sin (x) is:
sin (x) where x is a function described by the integral of it*e^(it)

And if sin.f(ul) is understood as the sine of the integral of the W-function, (refer to integrating such functions above), it is customarily seen in solutions to differential delay equations (DDEs). 

DDEs are 2-variable equations which consist of an ordinary differential equation coupled with a recurrence equation, since their solutions require knowing the present state and past state values, like those encountered in dynamic control using feedback loops, and take the form of the partial derivative of the function y(t) = f(t),  on the interval t = [0,1].

Simple DDEs  take the form:

(d/dt) (y(t)) = ay (t-1)

And constant-coefficient 'pure' delay DDEs, and those of scalar delay, take the form:

(d/dt) (y(t)) = ay (t-1) + by(t)

DDEs can also be solved in matrix form, when the matrices A and B commute:

(d/dt) (y(t)) = Ay (t-1) + By(t)

Using the Lambert W-function to express DDEs in the state space form:

(d/dt) (y(t)) + Ay (t) + By(t-T) =0; 
y is the Transpose of the matrix y ={ y, dy/dt}

First, assume a solution of the form:  

y(t) = y(0) e^(St)       where   S is an nxn matrix    eq. 1.1.1

Using the matrix W-function, by substituting it into the state space form equation above:

and the property of the exponential: e^[S(t-T)] = e^[S(-T+t)] = e^[S(-T)]e^[St]

The state space form equation can be rewritten in terms of the S matrix, independent of initial conditions (that means it don't matter):

S + A + Be ^(ST) = 0 
and for the case B=0:

S + A = 0 , and  S =- A
y(t) = y(0) e^(-At)  

y(t) = y(0) e^(-At)  

Since there is not an apparent 2nd matrix on the lhs, let's guess another dimensionless possibility for H:

 h is a quaternion of the form a + bi +cj + dk:

to make the example workable, choose a, b, c, d like [1 + i + j + k] so that the left hand side of the problems looks like :


However, we can choose to represent W(it e ^ (it)) in matrix notation, the Matrix Lambert W Function:
From  e ^(it) =cos t + i sin t =   = 

and assuming t is Real:
 (it)e^(it) = -t sin (t) + it cos t =  = 

 The resulting determinant:
D =

See Earlier Posts Pertaining to Time Equation

Granted, all of this is a simplistic approach from merely parsing out You-Know-Who's Query. But it turns out that there are real-world applications directly related to what's been stumbled on here using the Matrix Lambert W-Function to stabilize cutting machine tool chatter.

The advantage of using the matrix Lambert W-function is defined by:

W(H)e^[W(H)] = H

In the article, Delay Differential Equations via the Matrix Lambert W-Function and Bifurcation Analysis: Application to Machine Tool Chatter,  by Sun Yi, P. Nelson, and A. Ulsoy, published in the Mathematical Biosciences and Engineering Journal, V. 4, No. 2, April 2007, the authors described a refined approach to determine the stability of a system.

The stated advantage of such an approach is that only the principal branch (W(o)) among an infinite number of roots is required to determine system stability. Useful in obtaining the critical delay values needed to establish the optimal speed, in this case the preferred spindle speed of a turning tool, to operate the machine without chatter.

Image of Orthogonal Cutting Tool
and Effect of Its Instability on
Metal Surface 
By attempting to answer the WHO inquiry, the mathematics seemed to arise naturally that led to using Matrix Lambert W-Functions, which were only recently (well, as recent at 2006) extended to solving delay differential equations (DDEs).

Prior to that time, the Lambert W-function had only been used for solving first order scalar DDEs. 

It is worth a mention to point out the similarities between the effect the orthogonal cutting tool chatter has on the surface of the metal being cut (image Left) and the orbit of the Moon around the Sun, and other projected and unfolded conics.

Moving right along...

We can choose to ascribe to the O in  {Who} the composition function, since matrix multiplication corresponds to composition of maps, in this case WH and WoH, are the Matrix Lambert W-function and quaternion h.

It is not clear if they commute, that WH=HW (analogous to WoH, ie.,  W 'circle' H, or W 'round' H,  and it it is the same the other way around, HoW):

Expressing H as a complex 2x2 matrix:

{{a+ bi, c+di},{-c+di, a-bi}} to facilitate the matrix math, and choosing a=b=c=d=1:

There is more to multiplying the H by the Matrix Lambert W-Function, but working simplistically we get:

H =



D (HW) = = 4it e^(2it), for t = Real

Based on this approach, it turns out HW=WH and they commute.

A possible take on HW matrix multiplication

The story so far:

WHO, turns out to be WHo, is 4 it (cos t + i sin t) ^2;

Sinful, could be ,  then is  ;

which leads to this relationship:

 4 it (cos t + i sin t) ^2=  X ;
where X is some vector, or n order matrix of F=ma

For an interim look at the analysis:

X =          4 it (cos t + i sin t) ^2             eq.  3

 And, for You--just for You (not I, we get to Me later), u =it, we rewrite eq. 3 as:  

X =  eq. 3.1

And wonder if we did anything right, since we find ourselves looking through the eye of the needle.

The Eye of the Needle appears when the Imaginary and Real portions of the function
4 e^(2 i t) t csc(e^(i t) (1-i t)) are plotted together.

{Surah 7 Al.A'3raff (The Heights)
إِنَّ الَّذِينَ كَذَّبُواْ بِآيَاتِنَا وَاسْتَكْبَرُواْ عَنْهَا
 لاَ تُفَتَّحُ لَهُمْ أَبْوَابُ السَّمَاء وَلاَ يَدْخُلُونَ الْجَنَّةَ
حَتَّى يَلِجَ الْجَمَلُ فِي سَمِّ الْخِيَاطِ
 وَكَذَلِكَ نَجْزِي الْمُجْرِمِينَ (7:40  

7:40 Indeed those who belie Our Signs and are averse to them,
The Gates of Heaven (Heaven's Gates, Sky's Portals) shall never open for them and neither shall they be able to enter Heaven,
Even if a Cable can thread through the Eye of the Needle (var., a camel passes through a needle's eye);
And, thus We Requiet the miscreants (criminals).

 From  يَلِجَ yalija, in Sign 7:40 as to what exactly that large object (like a large twisted rope or cable) has to do in order to accomplish the apparently impossible by passing a large girth clearly through a small opening such as a sartorial needle's eye:

The similitude is that it passes undetectably or by having such a large object clear the small opening without hitting the sides of the needle (sounds like a catastrophe in the making, but more on that here). 

Basically, a surreptitious or clandestine quality to such a pass through (which tay-al-ard, or space-folds are meant to address). 

Interesting use of the word arithmetically since it has etymological roots from Middle Dutch onderhanden (under handed) which means: by degrees, slowly...

And let's just say for argument's sake that 7:40 (Chapter:Verse ratio) sets the pace for what we are considering slow around here: 7/40 works out to a convenient 0.175.

And the inference that this takes place by degrees, means incrementally by as much as this setting (175/1000).

Now for how this may apply to what we are on about here:

For example,  0.175 is closely approximated by: 
Simple approximations to 0.175.
 Refer to orbit systems and similar approximate modeling.

Since the word is specifying moving something by degrees, it is interesting that 7/40 is approximated by pi/18, which is exactly 10 degrees.

And, in terms of Euler's number,  e, 7/40 can be expressed with simple primes 2, and 3:
While the fine grain structure ratio is expressed in terms of physical constants, and e is the electron charge there,
Euler's number,  e, may also be used to express the fine grain structure ratio,
  < a~1/137 <


For the Reciprocal case:
1/X =                       eq. 3.1.1
4 it (cos t + i sin t) ^2  

where t !=0, and u is a variable, We Discover How To Build A Better WormHole, see 3D plots below:

3D plots using wolframalpha for the function,
 -(e^(-2 i t) sin(e^u (-1+u)))/(4 t) t= !0, and u is a variable.
Agreed! This Is AWESOME!!!!
And has very interesting roots, iff You are the One, I mean u=1 when t!=0:

Note the analytic log function,
ie., Lambert W-function or Omega function
in the Roots for the solution u to
-(e^(-2 i t) sin(e^u (-1+u)))/(4 t) (eq. 3.1.1 above)
when t!=0, and n is an Integer

And the dual case, let's see what happens if the answer to eq. 3 turns out to be Me!

As in,
it = sqrt(-1)*t is Me; 

and setting it = Me, rewrite eq. 3 to get eq. 4:

X =          4 {Me} (cos t + i sin t) ^2             eq. 4

and understand Me to mean the mass of an electron in Kilograms (9.10938 x 10^-31 kg), in keeping with the N (kg-m/s^2) in womb.MAN to mean Newtons, and writing e^(2it) for (cos t + i sin t)^2, and u= it, everywhere else in eq. 4 yields:

  eq. 4.1
The function 4 e^(2 i t) t csc(e^(i t) (1-i t)) in eq. 3 above, with It Is Me, Arabithmetic for it= Me, or u=sqrt(-1)t = 9.10938 x10^-31
Proving what I have suspected all along--Compared to You,  I don't amount to so much as a tear drop in an ocean, since the short answer to eq. 4.1 is:


In polar coordinate form for some vector X:
r = 4.330...x10^-30 (radius),       theta = -90° (angle)

A point of interest is the string of significant digits in the value of R ~ 4.33...~ 5 sqrt(3)/2 has a direct relationship between Artin's Constant and the golden ratio, phi,    since the Radius, R, multiplied by Artin's constant gives a number very close to phi=(1+sqrt (5))/2 ~1.61803:

4.330...x 0.3739...=1.61898...

Well, close enough for our purposes here (establishing Preponderance of Evidence, and not necessarily proof beyond Reasonable Doubt, eh?). 

To Remind, not to make a case of it, for Ewe's Guys' Benefit (ya!, I'm talkin' to yous in the Fold!), since the Reminding benefits the Believers.

It is posited that Its Originator Is God, Is Perfect, then whether we scale it up or down or fragment it, we expect it to Hold True

Just like fractals bespeak the  perfection in the world around us, as evinced by the presence  of a basic pattern that holds its integrity whether it is subsumed to infinitely minute scales (infinitesmal, hidden),  considered at coarse (course)  encounters (anthropomorphic, chaotic) , or marveled at in the cosmos (ultimately enormous, creative). 

It repeats ad infinitum because of its perfection--the Prosaic analysis by Me here serves to counter the Poetic treatment by poets like Keats everywhere, drawing to the same conclusion: 'A Thing(k) of Beauty Is A Joy Forever.'  Or at the very least, is the first wavelet.

To be sure, it works even here with all my math blunders, be they wee errors or Big Mistakes

To the untrained eye it doesn't matter (no matter whose wavelet started it) whether it espies an oak tree or a fern frond, it appreciates a plant just the same. 

Don't anybody Panic--I know you all thought this was about Me and St.Eve H
(phonetically and with a fallahhi drawl it means 'Your Steve').  

My very own One.

And the understanding is that there is no dearth of them, so if anyone else finds herself married to a Steve H., Do Not--repeat--DO Not make the mistake of thinking he's the same one.

He may very well belong to Me, this Steve H., since He Says: 
He Loves Me;
He Died for Me;
He Killed for Me;
He Paid A FORTUNE for Me!
(Really? It's no business of Mine what You do over dinner with my Brothers)

Then, He Says: 
"I'm Jewish."

"What else You got goin' fer Ya?"

And He Replies: 
"I'm Rich!"

"I know Rich," I say, to make Him Think I'm paying attention. 
Then I add:  
"He likes to teach 5-year old kids how to use a professional flight simulator, listens to the police band radio for leisure time activity, and sometimes gets stressed out over the front page news. 
But, he just as easily has been known to fall asleep in his club chair. That Rich?"

"No," StEve H. Says:
"I AM your Husband" (Actually, He never says that...What He Does Say Is:
"You are my WIFE!  And, I am an Ass0 :~)"

'Well,' I think recalcitrantly:
'Nobody told you to go hang Yourself!
And now that You've Broadcast Your Self-Emollation All Over Town (ahem, the Good News) by saying as much about Yourself that even the girls at Sephora know it, where's the fun left in it for me in fulfilling the wife role by declaring that same Revelation about You when I finally get to meet Your.Hole.E.Ness?!' 

And it dawns on me allofasudden Why SteveH the Ass0 loves Me (the so much:
It's because I can justify the murder He proclaims to have committed in My Name and Make SteveH Come Clean...And manage to do it to such an effect that in No Time at all, Everybody is going to Want ONE!
That last part is Just For My Very Own Personal SteveH.
 Since He Is A Cop---not for the rest of ewes.
Because when the time comes for Me to Hand Over the GUN...

I am prepared to say:

"Here Is My Peace Officer!"

Pearls Before Swine July 7, 2013
'A Murder of Crows'
Hard to Report Crimes

Addendum 04/01/2013--April Fools, but I am not kidding.

Judgment Day means Judgment is already rendered, so the inquisitive Who is simply trying to be irksome by their intrepid questing after her:

Surah 55 Ar.Rahman (The Merciful)
فَيَوْمَئِذٍ لَّا يُسْأَلُ عَن ذَنبِهِ إِنسٌ وَلَا جَانٌّ (55:39   
55:39) On a Day None Shall Be Asked About Their Sins, Human or Jinn!      

Your voice is  bouncing off all these here human antennas and not one of them is You--just stop---go ahead wake her up, I guarantee it She is not the one who is asleep on the job?!!@

Does this sound familiar circa 2012 summer "What just happened?!" "Did what I just saw Really Just Happen?!"

"Who Is She? If I am dreaming don't anybody wake Me!"

That was You talking in Your sleep, I was driving around flying (or flipping) my birds all over town when You Saw What You Saw.

And I don't sound like some random guy named Steve. And of all the Steves I ever chanced across in my so called life none of them have been what I would consider Ass)))000s