Showing posts with label Life After Death Experience. Show all posts
Showing posts with label Life After Death Experience. Show all posts



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 

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 isometrya 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.
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. 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 axisThen 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!


The Trip To A Museum

...or How To Keep'm Separated

And still Not Enough Distance:

43 Zukhruf (Gilded with Gold)

43:38 حَتَّى إِذَا جَاءنَا قَالَ يَا لَيْتَ بَيْنِي وَبَيْنَكَ بُعْدَ الْمَشْرِقَيْنِ فَبِئْسَ الْقَرِينُ

43:38 In Time (After some Length), when he comes to Us, he says: "Would that between me and you were the distance of the Orients! Such evil company!"


Forms, Shapes, Depictions, And Rides

There are compelling reasons not to be misled into thinking anything or anyone can actually ever usurp any kind of power from God; and why it is imperitive not to have any preconceived images of what God is.

Al-A'la (The Maximal (Uppermost))

(87:1) سَبِّحِ اسْمَ رَبِّكَ الْأَعْلَى
(87:2) الَّذِي خَلَقَ فَسَوَّى

(87:1) Glorify the name of your Lord, the Supreme (Maximal; Uppermost)
(87:2) who creates, and ‘sawa’ (delineates, makes, forms, describes, shapes, levels, squares, planes out, organizes, categorizes, arranges, ranks…)

Al 'Imran (Jesus' Family--The House of 'Imran)
(3:6) هُوَ الَّذِي يُصَوِّرُكُمْ فِي الأَرْحَامِ كَيْفَ يَشَاء لاَ إِلَـهَ إِلاَّ هُوَ الْعَزِيزُ الْحَكِيمُ

(3:6) He depicts you in the wombs (places of Mercy/Matrices) as He wills. There is no deity but Him, the Almighty, the Truly Wise.

( يُصَوِّرُكُمْ means to picture or imagine; no doubt where the phrase 'in his own image' comes from misdirecting us into thinking somehow God looks like a person and acts like one, but the true value of this phrase is that we are what God imagines us to 'Be'--if there is a 'person' out there that can do that-- create something from nothing but their imagination--I would most certaintly love to meet them--otherwise, let's come to terms with our own humanity and be grateful we think we are here).

As-Sajdah (The Prostration)

(32:9) ثُمَّ سَوَّاهُ وَنَفَخَ فِيهِ مِن رُّوحِهِ وَجَعَلَ لَكُمُ السَّمْعَ وَالْأَبْصَارَ وَالْأَفْئِدَةَ قَلِيلًا مَّا تَشْكُرُونَ

(32:9) and then He delineates (‘sawa = lit. levels; makes, forms, describes, shapes, squares, planes out, organizes, categorizes, arranges, ranks…) him, and breathes into him of His spirit: and He endows you with hearing, and sight, and hearts (sensitivity; feelings; minds); seldom are you grateful.

(Parenthetically, if the abortion issue means anything to you, you may want to study the above passage to try and settle when a zygote is just a clump of cells and when does it become a living viable human fetus)

Al-Hashr (The Gathering)

(59:24) هُوَ اللَّهُ الْخَالِقُ الْبَارِئُ الْمُصَوِّرُ لَهُ الْأَسْمَاء الْحُسْنَى يُسَبِّحُ لَهُ مَا فِي السَّمَاوَاتِ وَالْأَرْضِ وَهُوَ الْعَزِيزُ الْحَكِيمُ

(59:24) He is God, the Creator, the Maker, the Depicter! His are the attributes (names) of perfection. All that is in the Heavens and Earth worship Him: for He is the Almighty, the Truly Wise!

Nahl (Bees)

(16:8) وَالْخَيْلَ وَالْبِغَالَ وَالْحَمِيرَ لِتَرْكَبُوهَا وَزِينَةً وَيَخْلُقُ مَا لاَ تَعْلَمُونَ

(16:8) And (He creates) horses, mules, and donkeys, for you to ride and for their beauty; and He creates things that as yet you have no knowledge. (Some of which you now call UFOs—any guesses as to who the riders are?)
Now to proffer a few words of comfort to those among us who have actually been instructed to shoot them down and are now having an ‘aha! moment’; no worries really, among the riders could be your mothers and by far they make for safe targets because they don’t generally shoot back and what child doesn’t secretly harbor the fantasy of shooting their mom? In fact, the need to shoot one’s Mom must be quite pervasive as it provides comic fodder for prime time TV; Family Guy chronicles baby Stewie’s fantasy to do in his mom Lois at least every other episode.

While someOne goes to great lengths to ensure you have mothers, we all know they are the last people their children ever listen to; and that's why I questioned why I should bother at all (Michael) because a couple of years of diaper duty would have been absolution enough for me.

Al A'raf (The Heights)

(7:198) وَإِن تَدْعُوهُمْ إِلَى الْهُدَى لاَ يَسْمَعُواْ وَتَرَاهُمْ يَنظُرُونَ إِلَيْكَ وَهُمْ لاَ يُبْصِرُونَ

(7:198) and if you call them to guidance, they do not hear; and you may think they see you (pay attention to you) but they do not."

This last Sign is a tad troublesome since this particular convergence has been a difficult one. Understanding that the Ayat (Signs) can be understood on a multitude of levels, I think a practical explanation is called for at this time. First, like the others, Ayah (7:198) can be taken at face value and it might even seem a bit mundane; but please be cautioned that there is a deeper meaning.
The other day I was standing at the market service counter when a young couple came up to place their order. The young man stood close to the case so he could place his order and his companion took a couple of steps back in order to have a more panoramic view of what was on display in the deli case. A server called the next number and a patron whose number was called came over to the very spot that was right in front of the young man's companion; not only blocking her view and inserting herself between the couple, but seemed completely oblivious to the young woman now only about an inch behind her.

The young woman was so incensed at this patron's rudeness that she blurted out her frustration at being so completely insulted by what appeared to be such a total disregard for her 'space' and took a few steps away from the offender and around to my side; still muttering to herself how she can't understand how anyone can be so rude! The patron was in a state of absolute shock that this young lady was carrying on like that and the confusion registered in her eyes and the questioning look she shot at me, who happened to be observing this scene unfold.

I could tell it was not in the offended party's character that she was given to such a tirade, and it was painfully obvious to me that the patron clearly did not even see this young lady (tall as she was with very long, thick black hair--you would think no one could miss her) simply standing there when she cut in front of her. Despite my strong predilection to keep to myself I had to say something to explain to both of them what had just happened and I kept it in simple terms.

Patron: "What just happened?"
Me (as gently as possible): "She is upset that you just cut in front of her. She was standing right there."
Young Woman (still in a huff, embarrassed this is out of character for her): "How can anyone be so rude!"
Patron (still stunned, because she absolutely did not see her, but sincere): "I am sorry, I didn't see you standing there. I didn't mean to be rude."

The young lady collected herself and went back to the other side where her mate was standing, and the thoroughly bewildered patron moved away from them, having woken up to the fact that just moments before she was completely oblivious to someone whose physical stature actually dwarfed everyone else's in the vicinity.