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

Ahh 2B A Stah

I was trying not to post anything new in 2012 and simply spend the rest of my time completing earlier posts; some of which were set aside while new ones were started, some of which had work lost mid sentence and the material could not be readily recalled for completion.

But here are a few thoughts on what others (them) think.

Let me preface what follows by saying that I am not in the best frame of mind--hard day having to digest the confirmation that I am step-mother to my own children; my grandchildren are afraid to so much as look at me--God only knows what they are being told about me; my hair is falling out in clumps from spending too much time at 0G and not due to my jumping for joy, but being hopping mad; I still hear random individuals take the liberty of pronouncing my name to whomever/whatever Unknown is on the other side of the phone (Skype)line when I pop into my neighborhood Starbucks (I had avoided going there for several weeks and then when I ventured in again that Mr Oh!G still could be overheard doing the same); then to have that one individual actually wake me from my sleep by calling me from within my private room.


Look, if I so much as suspect that voice as coming from a man or woman I've come across I have no reason to trust them, because, well because this and still no reasonable explanation (so whoever knows this much about me is by default automatically implicated in the crime and that's why no signal from outerspace, see I can ignore them just like they did me and then some, because I can do it on multiple levels)!

I find myself still making excuses for noises and pressure changes in my car, trying to rationalize what's weird, and the flashes I see while driving or going about my daily so-called life are not because they are shooting my picture but whatever it is I know Who to thank for what I've been calling migraines.

So this post is all about apertures. Openings, or 3ayns, like our eyes where light enters, and anuses where skutt leaves, and why never the two 3'ayn shall meet.

Overheard at, where else but the salone of the 21st century, coffee shop a man was explaining to someone how it is the very nature of the human brain to be the center of its universe-- to make everything in the world about that individual and why everyone, no matter who they are, or what they say, all want to be a Star! Not a Planet, or Blackhole, or some other Space Debris, but a Star--and not as a destination-- no wonder we are all still stuck here on (multiple) Earth.

Spoken like someone who only knows everyone in Los Angeles. And this man's sweeping assessment of everyone's basic nature and true character is nothing more than the projection of probably his own aspirations onto everyone else.

After all if he wants it, then surely doesn't everybody else?

Are they any better than what he thinks?

Can they possibly be any different?

The Argyle Sweater Feb. 21, 2012
"Why Would Anyone Try Not to be Noticed?"

What? Why? Are they aliens?

Well, unlike him, I can't speak for everyone else. But some of us, me, a handful of friends, family, and acquaintences don't seem to want that. Some of us do-- the ones born and raised in LA, but on the whole we don't spend time even thinking about it. Not that we can't appreciate a Star when we see one. I enjoy a reason to dress up and see a show as much as anyone, but that  doesn't mean I want to be in every production!

My Mother, for example, all she is ever on about (when she catches sight of me, anyway) is 'Land! Land!' and I'm like 'What on Earth is Her preoccupation with Land?'

True, its rising up out of the Water is fascinating, but that trick got old after the first time.

Speaking for myself, its not so much what I want as much as what I don't or didn't ever want--any problems. Because then I would be forced to have to sit down and try to solve them and that leads to just one math mistake after another (and then HE wipes out the final touches to my antenna).

And for the gentleman who thought he was channeling my Father on his way out the shop by telling me to "Study!" That's like the last thing my Father would ever adjure me to do, in fact He once emphatically told me I do too much reading and studying and to make His point stick, He literally threw the book at me (it was Calculus).

"Books have led some to learning and others to madness."
--Petrarch

Lay On MacDuff

"Lay on, MacDuff, and damned be him who first cries ‘Hold! Enough!”

-Macbeth, William Shakespeare

…them’s fighting words?

Sounds more like poke'r to me.

(I Am my Father's daughter and, like Him, I, too, believe that Gaming is the only sport where you lose as soon as you sit down to play it, and in order to make real money You just gotta Earn it (as in work for it and not simply rely on the luck of the draw)).

“Who would want to hurt you?”
When the question was first posed over 15 years ago, my naiveté would only permit the following response;
"Duh--like I don’t know…”

But in retrospect the answer is more than likely, “Practically the entire human populace because I had to be the one to break it to them that for all their pageantry and eons of human evolution, they still haven’t figured out how to have sex—they go around big-footing it all over the world when the men can’t even make a conquest in their own bedrooms, being easily duped into believing otherwise; and their women have it in for me since, (apparently even Dr. Ruth did not venture into this uncharted territory), there are juicy signs as torrential as the Great Flood, and now the jig is up and they can’t fake it any more (like in the diner scene in the movie When Harry Met Sally--and unlike that film Producer's Mom in that same scene I Don't Want What She's Having!)."

(What does everybody think Rain songs on the Radio are all about—the weather? For that we have the meteorological forecast.)

...and, speaking of Meteo-rites, an alien take on their solar system...

Surah 34 Sheba (The Queen of She-Ba)

أَفَلَمْ يَرَوْا إِلَى مَا بَيْنَ أَيْدِيهِمْ وَمَا خَلْفَهُم مِّنَ السَّمَاء وَالْأَرْضِ
 إِن نَّشَأْ نَخْسِفْ بِهِمُ الْأَرْضَ أَوْ نُسْقِطْ عَلَيْهِمْ كِسَفًا مِّنَ السَّمَاء
 إِنَّ فِي ذَلِكَ لَآيَةً لِّكُلِّ عَبْدٍ مُّنِيبٍ  34:9  

34:9 Do they not see how much lies (open) between their hands and how much is (lies) hidden in the Heavens and Earth...(in other words, how little they see of what lies open and hidden in Heaven and Earth?); if We Willed We Eclipse/Cleave the Earth with them or Drop pieces of the Sky over them; Truly (Indeed), in these Signs (are) Every Servant (of God) Foretells/Predicts/Calculates/Is Penitent/Remorseful.

Penitent and Remorseful, sound a lot like Sad to me, and while it is True that '...you can get addicted to a certain kind of sadness (Song Lyrics from 'Somebody That I Used To Know') I, for one, do not enjoy being sad...but I should have figured out there was a problem much sooner, at the first hint that my friends thought they saw me coming in Orange when I know I was Blue.

But Colors are another subject altogether, it's much easier to just stick with the numbers..

"I can calculate the motion of heavenly bodies, but not the madness of people."
--Isaac Newton

Sign 34:9, taken as a simple ratio is 3.77777777....or Three (3) + (7/9). Nine we all know is 3^{^2}.
The fraction or decimal portion when dividing by 9 always given by a single repeating numeral; 1/9=0.11111...; 2/9=0.22222....; 3/9=0.333333...;...and 13/9=1.44444.....

In this case MOD(34, 9)=7, ie. 7/9 or a repeating decimal of 0.7777777...

Relationship Between Solar System Planets/Objects
With Respect to Mercury@ 1AU vs Earth@1AU
and the Lemniscate Constant

The first approximation as to why there may be something out there according to the Table Above. Assuming a progression or natural harmonic for the mean distance (aka semi-major axis of an elliptical orbit) of the known planets/objects in the Solar System, the product of the Lemniscate Constant (2.6225) and each planet/object's mean distance (using Earth as the basis for 1 AU) results in a value close to that planet/object's mean distance with respect to  Mercury as the basis for 1 AU.

This was used as a first order approximation since the Lemniscate ties in well with orbits/space/time  and the pattern emerged readily.

Using the conventional standard Earth mean distance at 1AU, then Mercury =0.387 AU x 2.6225 (the Lemniscate constant)= 1.015AU (giving the Earth Mean Distance by this convention, and about what it takes to make Mercury the convention for 1AU,  http://www.solargeometry.com/).

Since this also corresponded roughly to the mean distance of the Earth @ 1 AU, the way the table developed it turned out to be the 3rd object from Mercury, while still being the 3rd Planet from the Sun (ie., compare distances in column O_n vs column C_(n+3) vs D_n ).

The next outer planet Venus mean distance wrt Earth=1AU then follows from  0.7224AU (wrt Earth=1AU) x (2.6225)= 1.866 AU (Venus mean distance wrt Mercury=1AU). The expectation being a value close to 1.9 AU should correspond to some planet/object y for this pattern to hold in Column C Row 7.

Then to keep an even distribution and give Mars as the 3rd planet from   'something (phi= j)'  between Mercury and Venus is expected to be near 1-1/3 AU (wrt Mercury @ 1AU s.t. the mean distance wrt Earth @ 1AU  in C3 is (1.33../2.58..) approx. 0.516 AU x (2.6225)= 1.3533 (a mean distance that roughly corresponds to Mars mean distance in Column C Row 6, according to this pattern (distance in O3 vs C6)).

The 1-1/3 value was not selected at random (refer to the Lusona lesson). The idea was to keep the distribution about as even as possible and keep as much symmetry in the distribution as possible.

Since a rough estimate for the mean distance to a Kuiper Belt object was taken as a round number, 50 AU wrt Earth @ 1 AU, worked out to approximately 129.17 AR wrt Mercury @ 1 AU and when 50*the Lemniscate constant worked out to 131, a number close enough to 133 to keep the symmetry given the breadth of the field of such objects,  this was in good enough keeping (both in the progression and geometry) to guess something 'phi' at 1.3333 AU (in Column C Row 3). It also didn't hurt that 133/7 = 19 (see further down the post).

(I hope You are reeling with awe regarding the shallow depth of Knowledge I have in Astrophysics; but, since I can't even do simple math or hold a number in my head longer than a femtosecond,  this is what I can manage).

Pursuing this method, objects/planetoids were expected at locations j= x, y, z, aa, and bb. The pattern that emerged simply using the Lemniscate constant as a multiplier holds at least up to mean distance of Kuiper Belt objects from the Sun.

Unlike the finesse required for Rocket Science, ever the tactful one, this is more of  a bludgeon approach to introduce an 'error' (j, x, y, z...) and check for 'ringing' kind of engine.ear.ring---(Where Can I Go to See What You *(all) Got?).

The idea is to keep some constant multiplier (in this case 2.6225...that would give the next outer planet/object approximate mean distance in an orderly fashion, and keep percent errors as close to 0 as possible for known planets/objects/'guesstimates'.

--What's the use? There ain't no use, if it's gonna hit, it'll hit--this is simply a pain-coping mechanism short of resorting to illicit drugs.

Flatlander Fred's Encounter With A Sphere

A Meaty-ORE from RealmSpace is About to Hit Flatlander Fred ’s Humble Home.

But, as You (ALL) can see, that's not really what a 3-D sphere looks like to 2-D Fred the Flatlander.
To Fred sitting in his living room one day, getting an unexpected visit from the sphere from ’outer space’, looks like it passes through the air right before his eyes.

To him, it will appear as if a circle came out of nowhere and materialized right before his eyes.

It expands rapidly, and Fred fears that its going to devour him and his house with him.

But to his relief, its growth slows down, then stops, then the circle starts to recede (shrink) again, but slowly. Then it starts to shrink faster and faster until it quickly disappears.

(Drawings and Text from Higher Dimensions. Find even More skillfully executed drawings and adventures of Fred, Emily, and Bob at Higher Dimensions.)

Mean Planetary Distance From the Sun vs Quotient of 19

For a second approximation, choose to represent each planet/object mean distance from the Sun as a quotient of 19, the farthest column shows the percent error between the quotient (calculated) and the apparent mean distance for each planet/object.

Well, why 19?---one finds themselves asking.

The easy answer is 'cuz the source under consideration says so...See?--Right here (Sign 74:30).

There are other more pragmatic reasons for choosing to represent each distance as a quotient of 19.

• Most cases divide by 19 gives an irreducible fraction or a repeating decimal of period 18.
• 19 in binary form is 10011_2
• 19 and 17 form twin prime pairs.
• 19 is the exponent for the Mersenne prime 2^{^19} -1=524 287, associated associated with the perfect number 137438691328 = (2^{^19} -1) (2^{^19} -1).
• 524 287 binary form representation is 1111111111111111111_2. (presumably 1400++ years ago there were no computers at the Prophet's disposal, but now that we have some laying around maybe the binary form is of some interest and may give some interesting insights.)

Note: Pertaining to 17 as a twin prime to 19, an inner planet/object distance wrt Mercury @ 1AU x (17/9)=1.8888... holds a similar pattern as when using that planet/object's mean distance wrt Earth @ 1AU x the Lemniscate constant in the previous table; such that Mercury @ 1 AU x 1.88 = 1.88 (approx. Venus (1.86) wrt Mercury at 1AU); x @ 1.33 x 1.888...=2.52 approx. Earth (2.53) wrt Mercury at 1AU; Venus @ 1.86 x (17/9) = 3.5 (near Mars (3.9) wrt Mercury @ 1AU; Mars @ 3.9 AU x (17/9) = 4. 87 (about what is expected at location y (5 AU wrt Mercury at 1AU, etc.). The table is not shown in full in the interest of conserving space and since those values can be readily generated, simply using 19 as the multiplier, (ie., 133/7, but since that is a factor of 10 too high 19/10 x mean distance wrt  Mercury at 1 AU, would be the equivalent multiplier).

Using the Magic Angle M(theta) as an Iteration for Mean Distance Formula of Solar System Objects

An interim step using the Numerator for the Mean Distance as a Quotient of 19 was to derive the mean distance wrt the Magic Angle

q_M

q_M     =ACOS(1/Ö3)

The formula in column H is mean distance in (column E_n/2.1)/(8+ACOS(1/Ö3)). This gives values for mean distance of each planet/object as a function of  (8+q_M    .).

Each mean distance in H is given by the numerator of the mean distance expressed as a quotient of 19 (Column E)  divided by 2.1*(8+q_{M .}).

The magic angle is typically given by Sec^{^-1}  (Ö3) (for more on religious/spiritual/Masonic associations pertaining to Ö3) refer to Vesica Piscis (now We know what that Lost Bunny of the Apocalypse and Guam has been on about these past few weeks in the Prickly City Comic Strip).

While Arc_secant is typically an inverse trigonometric function used in the States, elsewhere it is simply expressed as the inverse cosine function Arcos (1/Ö3), (ie, 54.740 degrees or 0.9553166 radians; 54 degrees, 44 arc minutes, 24 arc seconds; or RA 3 h: 38 min: 58 sec).

A finagle factor (divide by 2.09, 2.1 or 1.5), while serving as a simple multiplier to approximate the mean distance relative to the magic angle, is a number that also relates to the packing density for body-centered and/or face-centered/or simple-cubic lattices.

While at first appearing to be quite random, this factor of 2.1, is really nothing other than 19/9 = 2.11111....(see twin primes 17 and 19 above, the ratio of each to 3^{^2} , the Gee_ometry of the Solar System,  and how they relate to each other here).

("So What?" You Say, "I can find some relationship between any 2 somethings!" While this is true, it is more difficult to find and keep relationships between sets of somethings that make sense Math-wise--that can only happen by Design and when done right it can be made to look like an Accident--See Lie Groups, Quotient or Factor Group, symmetry, continuous transformation isomorphic/homomorphic/kernel--->pre-image_null space+zero point field)

Solar System Planetary Distance From the Sun vs Root Approximations

The mean distances are represented as approximate roots and what emerged was interesting in that the golden mean (j) figured in some of them and more to the point was the fact that p/4 (ie. 4/p, or specifically (4/p)^{^2} ) also emerged as a convenient way to represent the mean distance of known planets and objects in the Solar system.

Euler's number was expected to emerge as well, when finding ways to set Mercury to 1AU, so wherever possible, it was attempted to work e into the formulas, but it didn't seem to fit naturally until resolving Kuiper Belt objects with this approach.

Sure we can do what Newton and Einstein and all the other highly respected physicists did, and we are familiar with their work, but can they predict what is coming out of nowhere based on their models?

Ducks Window Shopping Along the Boulevard
Venice, CA Feb 26, 2012
Reported to have Obeyed Traffic Rules,
Crossed The Street Using The Crosswalk

So, since God is Perfect and the News is All Good, just for kicks, a perfect Solar System should be well represented Mathematically without resorting to all the mind bending physics rigmarole, because I once was a highly developed thinker, but now I am retarded--especially after the recent 3-day 'migraine' layover--I think my brain is now Duck Soup, suited to simple tasks-- like shopping.

What's of interest here, is that in order for the pattern using prime square roots (Ö2, Ö3, Ö5, Ö7...), j, p and e to work, the Kuiper belt objects were refined to a mean distance of about 127.7(002)... which kept the percent error between the mean formula distance and that mean object distance as close to 0% as possible with a rather simple relationship that followed from using j^8 * e; and the number 127.7(02) also fit the pattern using p as a formula mean distance wrt Earth @1AU, which worked out to 8425/(21p)=127.702.

The root formulas had led to finding the magic angle relationship f(Ö3) in the previous table which bolstered guess-timating something of interest in the area of the Kuiper Belt objects close to the 127.7 AU wrt Mercury@1AU (or about 49.438 AU wrt Earth @ 1AU).

For the purposes of this exercise that distance for a Kuiper Belt object was revised from the first approximation of 133 AU to 127.702 AU (hopefully a refinement).
__________________________________________
It's especially exciting to see that p/4 (or (4/p)^{^2} ) since this intuitively means we are dealing with solid angles...wait while I check because I don't remember exactly why I thought this to be so exciting...

I even remember thinking seeing this (4/ p)^{^2}   to be elegant at one point....
_________________________________________

The Lemniscate is an inverse curve of a hyperbola ( the Lemniscate of Bernoulli or 'pendent ribbon' being the familiar case---> sideways figure 8, a special case of the Cassinin Oval), so where 2 branches of a curve would asymptotically fly off to infinity as in the hyperbolic case, the Lemniscate as the inverse of such a hyperbola 'knots' or 'ties' the two ends together (so to speak, see reference heavens/knitting/intertwined/woven paths) 'binding' it to a closed path where it may 'curve' back on itself.

Other inverse curves of the hyperbola include the limaçon, and the strophoid (or 'belt with a loop', of which there are two types, the oblique strophoid or the right strophoid--similar in shape to the early Christian symbol Icthus). The right strophoid or foliate curve is also called the  logocycle curve properties include: forming the basis for deriving logarithms, is its own inverse curve, and has a total area A=4a^2 (the square of the semi-major? axis of the parabola), normals to the parabola are equal like radii are equal for a circle.

That the logocycle curve is called just that probably stems from its utility in deriving logs (logarithms), since the word logos originates from the Greek verb 'to count.' And it probably is no mere coincidence that the early Christian symbol Icthys (the fish)  is the shape of the logocycle curve. (He wonders why I try so hard when i know i am not even connected to the internet---but, did you hear what's playing on the radio, see what's on TV, listen to what they're preaching from the pulpit?--go ahead, keep trying to make me die (again) laughing).

Early Biblical translations of the nature of Jesus reflected in their understanding of 'In the Beginning there was the Word (Logos), and the Word (Logos) was with God, and the Word (Logos) was God.'  An attempt to understand a difficult concept about dualism.

More about the possible connection between Logos, Logocycle Curve, and the Transfiguration/Crusifixion/Resurrection of Jesus   (http://apageinthelife.blogspot.com/p/logocycle-and-transfiguration-of-jesus.html).

In 'Real World' terms this would imply that Time, while understood to be infinite, has a nature by which it can and does 'curve' back onto itself (The Equation of Time), and its 2 ends meet in some manner, much the same way a hyperbola inverts to a Lemniscate. (And yes, in someways  just like the Tide washes in and out).

Or, how a simple harmonic wraps around or projects from a developmental surface, such as a cylinder or cone, to form such curves.

This further implies that Time's asymptosy (too tempting not to use such a word given its definition, Asymptosy: A useful yet endangered word, found rarely outside the confines of the Oxford English Dictionary) is in fact not a direct 'one-way arrow' as we are led to believe by our limited faculties and life experience, but rather that it approaches the 'ideal' final limit, or its 'asymptote' arbitrarily closely without ever meeting or crossing it, according to the very definition of what it is to display asymptotic behaviour.

This asymptosy or arbitrary, random walk (like the shopping ducks appear to be doing unless someone notices they use the crosswalk), verging on the threshold (the ceiling, or boundary) is what we would call a 'meandering' path'...a paradox about the infinite in finite space-time similar in scope to the Diagonoal (Coastline) Paradox.

{The etymology for asymptotic from New Latin *asymptotus, and Greek asymptōtos;   a- not + sympiptein to meet, ie.,  not meeting, And from a- "not" + syn "with" + ptotos "fallen," verbal adj. from piptein "to fall", ie., not falling together. More to the point here is 'petition' as derived from 'piptein' ; "a supplication or prayer, especially to a deity," from O.Fr. peticiun (12c.), from L. petitionem (nom. petitio) "a request, solicitation," noun of action from petere "to require, seek, go forward," also "to rush at, attack," ult. from PIE base *pet-/*pte- "to rush, to fly" (cf. Skt. patram "wing, feather, leaf," patara- "flying, fleeting;" Hittite pittar "wing;" Gk. piptein "to fall," potamos "rushing water," pteryx "wing;" O.E. feðer "feather;" L. penna "feather, wing;" O.C.S. pero "feather;" O.Welsh eterin "bird"). Meaning "formal written request to a superior (earthly, but in my case Not).

The Argyle Sweater 02.13.2012
Scott Hilburn
"Get The 'L' Outta Here!"

And as such serves as the premise for this Letter from Multiple Earths--a supplication to God to get me the L out of here (it was some time ago that I got the hint that prayer is no longer necessary, I guess I reached a point where it won't do any more good so I figure it shouldn't hurt to just ask, again) because we did not fall together And I stand by my claim that We did land together, but He ditched me--on more than one occasion, without any explanation or good reason.

But if I have to be the one to come up with a reason (read Excuse) for this (hurtful) behaviour, it may have everything to do with asymptotic direction after such a 'landing'-- one in which the normal curvature is zero. Such that a point on an asymptotic curve (or line), is in a plane which bears both the curve's tangent and the surface's normal (perpendicular) at that point. The curve (or line) of intersection of the plane and the surface will have zero curvature at that point.

Asymptotic directions can only occur when the Gaussian curvature is negative (saddle) or zero (flat).

In the case of negative Gaussian curvature (the saddle), there will be 2 asymptotic directions and these directions are bisected by the principal directions; {which could explain Our Parting of the Ways.}

Asymptotic directions at a Saddle Point (Gaussian Curvature is Negative)
 are Bisected by the Principal Directions

(Michael, I know 1992 was a spoiler alert and I don't even have to pack, I just need to go and seeing how SomeOne grounded me for these last 2012-1996/1997 number of years, I Respectfully Request that You Bring the 'Car' Around and Collect Both Me and My Daughter, I Know my Son has indeed Gone On Ahead of Us--I'm not trying to be funny here).

The Quranic reference for norms (normals, ridges) at 7:46, 7:48, 7:89, (for the return; 7:168, 7:169, 7:174...35:4...

Now for Sedna...

Mean Distance Planets/Objects in the Solar System vs. 19 vs. Sedna

I don't have an exact equation for the orbit of Sedna, presumably someOne else has already figured that one out.

But working with area graphs based on the emerging pattern developed when dividing mean distances by 19, it is expected that someThing of interest will occur (if it hasn't already) at approximately 375 AU (wrt Mercury at 1 AU) when Sedna is about 54 to 55 years (c 2130 ) past its Perihelion (which is supposed to be c 2075), refer to Column P row 18 in the Table above.

From the above table mean Distances in Column D are a function of Distances in Columns O & P, in that the second outer Planet/Object is a function f(inner planet/object) s.t. D_n relates to D_n+2 directly. So, with this 'squishy' predictive algorithm it points to something (in the gap/Mah) in Column D 13 ~ 37.4 AU is related to some trans-Neptunian object ~ 72 AU wrt , and that there may be something related to this at a distance approximately 131 AU, (ie., between Kuiper Belt objects (~127 AU) and where Sedna orbits c. 2008/2012 (~224.5 AU - 250 AU), (average distances given wrt Mercury @ 1AU),---go Figure!

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

This post started off with a quote from Shakespeare's Macbeth, a play about a Scottish Thane, and appropriately so, as the History of the Christian Church in Scotland is consequent to the works of Saint Columba (one of the 12 Apostles of Ireland whose name, closely affiliated with the Scott Clan Malcolm aka MacCallum, derived from 'Colum Cille,' from Gaelic/Erse for 'Dove of the Church').

The Arabic for MacCallum sounds like , مكلم , 'm.k.l.m' which carries the meaning of having been 'Spoken To' and the understanding is that 'God Spoke To' one of them; and if God Spoke and Malcolm/MacCallum listened to Him that would make them Isma'3liya and would explain how these two Clan names are affiliated to each other.

{I'm certain God Met with better Success Speaking to Malcolm than I did with the Malcolm I tried to speak to recently, who was conflicted whether to 'break the ice?' or 'not break the ice?' So, I went waaaayyyy out of my comfort zone to make it easy for him and he let me know that he just didn't want to be bothered, (maybe it was his bad back talking, but I'll not be doing that again any time soon---hmmm, something intriguing about these cranky 'old' men 'though (read 'men of Olde')).

Both the Biblical names Jonah and Jonas share a Hebrew etymology for Dove, as does the Pleiades star cluster, 7 or more stars visible to the naked eye, that are associated with Sailing probably due to the onset of Navigation season upon their Helical Rising.

This narration, about the connection between the Scottish Clan Malcolm (derives from 'shaven head,' or 'priest') and MacCallum, Saint Columba, the Early Christian Church, the Dove, Sacred Geometry, Architecture, and other Symbols related to Hidden Knowledge (The Occult) is all the more curious given Heraldry's deep ties to Scottish Shields and Crests (Coats of Arms) and the emphasis Freemasons place on such Symbols/Signs/Representations.

To tie things up, the significant connectivity between the various threads of surface elements gleaned from this cursory study reveals some interesting details as to how they are intertwined. There is no telling what Revelation may be had from a comprehensive examination of just the elements mentioned here, if one were inclined to dig a little deeper into the Mystery (like, 'Where'd they go?!')