Someone Started A Rumor

What is it about Americans that the 2 most often repeated phrases are "I'm sorry," and, "I love you."
Do you know what that sounds like to an alien?
It sounds like this; "I'm sorry I love you!"

And the alien can merely respond by saying, "My condolences, I understand your WIFE is a Muslim."

SomeOne searching 'been let down quotes' and 'you let me down' from unknown.unknown isp, then all traces of it vanished (and, howdie-do to our mangled-wire computer cousins at the US Army Signal Corp).
Not because there is any reason to suspect that being the case, but more than likely because someone started a rumor...that's why?
And it wasn't me. Nope, despite what anyone says I don't think I'm too good for You.
And if the let down has anything to do with my performance to demostrate my range, it was a training exercise-- putting a young-sounding voice to good use; and if my faulty memory serves, it culminated in the biggest bust of a worldwide child trafficking ring a few years later.


The phone records and chatroom snipe are probably still on your desk if not your top file drawer (and it was my cousin, Joey?, pointing me out to You in the middle of that unpartitioned office area, going through my paces on that particular afternoon--so, if I thought there was anything to hide I would not have been doing such a great job in a wide open common work area--with me being the only female in a 'bullpen' shared with 7 other male engineers, that's why it was called the 'bullpen').

And if You want to act like You don't know exactly what it is I am talking about then You deserve a bigger Oscar than the one I should get for my following Your 'I need you to go on sinning and grinning' acting direction from You Know Who?--You!

There really is no reason for me to live under such uncomfortable conditions, but seeing as how I don't even get what I work for and earn, I figure it highly unlikely that I can get what I simply ask for--not because I need any more lessons, but because I know there are more Powers at play than what those around me perceive.

For example, I have known that I am on the federal? payroll in some capacity as a government Annalist/Analyst since at least as far back as 2007 (maybe 2006) but I have yet to see a single penny of it--whatsamatter, having a little trouble making sense of the cumulative time?

See? I warned You--can't afford me?


Times like these I wonder why our family can't have our piano recitals in concert halls, like other families. (I know, it wouldn't be fair when Gabriel has more talent in His left nostril than the entire population that ever was or is or will walk the Earth, combined).

"I sometimes think we must be all mad and that we shall wake to sanity in strait-waistcoats."--BRAM STOKER, Dracula

In an ideal world (Heaven) I should be compensated for exposing my (hare) brain for Your consideration on at least the same par as world class models get for exposing their...their...their wookies (ie., other admirable/bankable hairy parts on earth).

Surah 60 Al.Mumtahhineh (The Examined One, Those Tested)
يَا أَيُّهَا الَّذِينَ آمَنُوا
 إِذَا جَاءكُمُ الْمُؤْمِنَاتُ مُهَاجِرَاتٍ فَامْتَحِنُوهُنَّ 
اللَّهُ أَعْلَمُ بِإِيمَانِهِنَّ فَإِنْ عَلِمْتُمُوهُنَّ مُؤْمِنَاتٍ
 فَلَا تَرْجِعُوهُنَّ إِلَى الْكُفَّارِ لَا هُنَّ حِلٌّ لَّهُمْ وَلَا هُمْ يَحِلُّونَ لَهُنَّ
 وَآتُوهُم مَّا أَنفَقُوا وَلَا جُنَاحَ عَلَيْكُمْ أَن تَنكِحُوهُنَّ إِذَا آتَيْتُمُوهُنَّ أُجُورَهُنَّ
وَلَا تُمْسِكُوا بِعِصَمِ الْكَوَافِرِ وَاسْأَلُوا مَا أَنفَقْتُمْ وَلْيَسْأَلُوا مَا أَنفَقُوا
 ذَلِكُمْ حُكْمُ اللَّهِ يَحْكُمُ بَيْنَكُمْ وَاللَّهُ عَلِيمٌ حَكِيمٌ  (60:10

 60:10 All You Believers (Faithful)! When believing women come to you as fugitives, examine (test) them. God Knows what's between them (among them). Then, if you ascertain them to be  believers (faithful), do not send them back to the disbelievers (infidels). They are no longer lawful to the disbelievers (unfaithful), nor are the disbelievers lawful for them (any longer). And give them whatever they may have spent. And it is not a sin for you to marry such women when you have given them first what they have earned. And do not keep (hold onto) defending disbelieving women; nor ask for (the return of) what you have spent (on them); and let the disbelievers ask for what they have spent (the are entitled to what they have spent). That is God's Judgment. God Judges between you. And God is Aware (Knowing), Wise.

But, fair is fair, and my Father predicted that I won't fall for that little beauty trick either (Really, I overheard Him on my way out the sports club telling someone He has every confidence I can pass that test, too!--I don't recall Him laying any odds on it, though.)

Check it out...Testing, Testing...
Surah 18 The Cave
إِنَّا جَعَلْنَا مَا عَلَى الْأَرْضِ زِينَةً لَّهَا لِنَبْلُوَهُمْ أَيُّهُمْ أَحْسَنُ عَمَلًا 18:7
18:7 Indeed, We Created everything  of Beauty on Earth to Test people as to which of them is Best in Conduct

( I passed this Test with flying colors, especially the night of Jan 13, 2012, when a drop dead gorgeous blond was openly flirting with me as I worked deligently on a business letter that was to be only 'a couple of paragraphs' and turned out to be 1600 words.
Don't get me wrong, I was flattered to no end--especially since the last time that happened I was 16 years old---now that I'm a semi-centurian, her attentions didn't quite ring so True.
Besides, that's a no-go for me, seeing as how I stated my position about Women earlier and found it to be much in keeping with WC Fields' feelings about Elephants.
Moreover, if they also happen to be anywhere nearly pretty enough for me to sense any kind of familial connection, then nothin' doin' --sis, 'cuz, G-Aunt, hoaxter!--And the real Killer to this non-starter Test is, I've openly stated where my true passions rest.)

Surah 20 Ta-Ha (Can You Hear Me?  'طه')
وَلَا تَمُدَّنَّ عَيْنَيْكَ إِلَى مَا مَتَّعْنَا بِهِ أَزْوَاجًا مِّنْهُمْ زَهْرَةَ الْحَيَاةِ الدُّنيَا لِنَفْتِنَهُمْ فِيهِ وَرِزْقُ رَبِّكَ خَيْرٌ وَأَبْقَى 20:131
20:131 And don't strain your eyes in longing for the splendour of the life of this world, things We have given for enjoyment to matched pairs (married couples) of them through which We Test them: but the Provision of your Lord is Better and More Enduring

(Another gimmee---what splendour are we referring to exactly? Hauling his laundry hamper up and down 2 flights of stairs while carrying his baby full term because he's too special to help with it or that he never reciprocated any of the good she's ever done for him or the support she freely gave him because he somehow finds it acceptable to abuse the 'now found to be mentally ill for saying she suffered a chronic toxic exposure from working in a sick building for umpteen frickin years?" and threatening to never let her see her children again if she so much as flinched at the despotism of living under his rule now that he would never allow for a divorce and use emotional blackmail to keep her in check---yeah, if I was God and ran this kind of test on someone, I would ...deleted for seeming contemptuous).

Surah 23 The Believers (Faithful)
وَلَقَدْ أَخَذْنَاهُم بِالْعَذَابِ فَمَا اسْتَكَانُوا لِرَبِّهِمْ وَمَا يَتَضَرَّعُونَ 23:76
23:76 And We Tested them through suffer­ing/trials, but they did not humble themselves before their Lord; nor did they ever pray (entreat/plead with Him)

(For this one, I get a Gold Star. You wanna know why? I actually saw and heard the Witnesses offer to give You a front row seat to see Me Down On My Knees; apparently, I was doing it quite a bit for some number of years that You could catch that show with some regularity--I only stopped when I got the signal that it was pointless beyond a certain threshold, see 15:98-15:99 below.)

Surah 29 The Spider
أَحَسِبَ النَّاسُ أَن يُتْرَكُوا أَن يَقُولُوا آمَنَّا وَهُمْ لَا يُفْتَنُونَ (29:2)
وَلَقَدْ فَتَنَّا الَّذِينَ مِن قَبْلِهِمْ فَلَيَعْلَمَنَّ اللَّهُ الَّذِينَ صَدَقُوا وَلَيَعْلَمَنَّ الْكَاذِبِينَ (29:3)
29:2 Do people think that they will be left (at ease simply) because they say, 'We believe', and that they will not be Tested with hardships?

(Nope, never thought that for a twinkle, but I Never thought it would drag on forever, either, because beyond the first 5 Earth Years, that, too, became pointless!
I am not doing the waking up in a hospital bed Men In Black thing, and I am not doing the Groundhog's Day thing, and I am not waking up to any walk throughs of any other scenes from any movie that was ever made or screenplay that was so much as even accepted on spec, okay--that's it! I've Had it- I had it when I called Him a RedHead and He corrected me to say that Tawny is in fact the more accurate description of the color (LIKE a LION)).

Surah 44 Smoke
وَآتَيْنَاهُم مِّنَ الْآيَاتِ مَا فِيهِ بَلَاء مُّبِينٌ 44:33
44:33 ..and We gave them such Signs as would clearly presage a Test 

(I got the Signs, all right *alright, to the effect that I started a diary, and a blog to preserve them for all posterity & what could be a Bigger Better Betoken than THE Michael Himself announcing His Presence- that was not a Sign to Presage a Test in 1992, that was like AN ANNOUNCEMENT, but I still wonder, why Me? ---there are definitely prettier, smarter, richer, taller, thinner, more powerful people--and we still have a President to the United States, or do we? And of course, those who drive nicer cars.
What? Did the world run out of virgins?
I'd already had a kid or 2; now I hear I have over 100--not bad for a woman whose own husband hasn't so much as dated her since their 7th anniversary.
Can you even imagine what that can do to a woman's self image? Let alone, anyone's ego---psshhaw, nothing!
I keep pretty busy and I still prefer being a female to being a male; if not for the fact that we don't sweat as much, than for the mere frilly lingerie incentive alone.)

Surah 72 Jinn
وَأَلَّوِ اسْتَقَامُوا عَلَى الطَّرِيقَةِ لَأَسْقَيْنَاهُم مَّاء غَدَقًا  72:16   
لِنَفْتِنَهُمْ فِيهِ وَمَن يُعْرِضْ عَن ذِكْرِ رَبِّهِ يَسْلُكْهُ عَذَابًا صَعَدًا 72:17
72:16 ...had they but tread firmly on the right path, We would have showered them with Abundance
72:17 As a Test to determine which of them would turn away from their Lord; He will thrust such (as turn away) into ever increasing torment.

(This one leaves me in a Quandary.
I tread the path, as right as it could be in the mind of a neophyte.
If we were talking averages, like engineers are wont to do, I'd say better than the average of what I saw going on around me (note, better than average, not better than everything and everyone---averages are more meaningful when we are taking a populatoin of 7 billion, because any 1 Event (Person/Thing) in and of itself may be considered as a statistical OUTLIER!
Yet, y, y, y the increasing torment?--I passed all of the above tests, and not only did I submit/surrender/give up without prompting the first time, but I tried to do it again a few weeks ago--You may remember, I even waited in the cold night air for SOMEone to haul themselves in for me to SUrrender to, and they Flaked, giving me to understand that my Unconditional Surrender is not accepted under any terms---I must have really ticked someOne off.
I now consider that my major life achievement---now, if I could only figure out Who that SomeOne is/was and where they're hiding.)

And if the disappointment stems from my having stopped praying, it's only due to this little love note:
15:98-15:99 ...pray until ....Can You guess how I interpret 'certainty'? ...
What is there left to say?

That this is how much injustice has to be tipped against me in order that they keep breeding and breathing?

... Want another demonstration?

Sasha, tell us what book you're reading at breakfast table and your sister can share her plans for running for office?

الْيَوْمَ نَخْتِمُ عَلَى أَفْوَاهِهِمْ وَتُكَلِّمُنَا أَيْدِيهِمْ وَتَشْهَدُ أَرْجُلُهُمْ بِمَا كَانُوا يَكْسِبُونَ
(36:65)
This Day We Shall Set a Seal on their mouths
but they will speak to Us with their hands,
 and their feet shall bear witness to whatever they earned in Life.
(36:65)

---
My hands r not tied, I'm free

It's not that I can't, I won't

I am not poor, just broke(n).

My G-Aunt keeps wanting to chime in with, "You know, Dear, the boys keep saying it's a sin to talk about it; but, just between us girls, headaches are a lot sexier on the Men."

I hear Him Say, 'Some fisherman you turned out to be when your net comes up empty time and again'.

I am more a 'catch and release' kind of fisherman...or some such 'sort' of thing.

And as for opting to pursue some 'weird dream' rather than to open my eyes to what's going on around me, I don't think I am as blind as some would like to believe. My 'weird dreams' manifest in physical space and time.

Take for example the image on the right--not a metaphor, but an event:
Location: ~ 34.07573, -118.38503  (~ 34° 4' 30.965" N     -118° 22' 51.363" W )
Orientation:  SSW? (same as that of the Roman reception desk)
Date: May 17, 1997
Time: 6 - 7 pm

UFO and Related Sightings Surrounding 'the event':

NEW BRIGHTON UFO SIGHTING

On April 25, 1997, the night more than 30 UFOs were seen over New Brighton, Minnesota, just north of the "Twin Cities" of  Minneapolis and St. Paul a sky watcher observed 3 UFOs in the same binocular field.

Over a course of several months… avid sky watchers have observed extremely high moving objects which traverse the sky in a few minutes…they appear solid, self-illuminated and round. These objects…named 'High Movers'...are moving in a N-to-S or S-to-N direction, with slight east and west variations… not consistent with satellites.

"Now, here is what is interesting,” an observer said, "all but two (of 7 he saw)  were moving to the northwest, towards Minnesota!... one moving to the northwest about 9:45 p.m… just as it was about to drop below the horizon… another moving near it, more to the east.. was amazed to have two in my field of vision at the same time, since viewing through binoculars greatly restricts the field of vision. A third High Mover (UFO) streaked past both of them.. I've never seen three in the sky at once...much less in the same binocular field of view."

COLORADO PILOT MYSTIFIED BY STRANGE RADIO CALL

On Monday night, May 12, 1997, a Colorado pilot was flying near Walsenburg (population 3,945) when he picked up a strange call on his radio.

"I was flying in clear VUCU sky (VUCU stands for "visibility unlimited, ceiling unlimited") when I picked up a weak communication on VoiceCom 121.5,  the common-use emergency channel… always monitored by commercial and most large private aircraft with more than one communications radio,” the pilot reported.

"As well as I could, I was able to make out someone at Flight Level One-Two-Three-Five Hundred (123,500 feet or 37,424 meters--J.T.) requesting 'immediate traffic in area.' There was obvious anxiousness in his voice, and he was talking to Air Traffic Control," he added, "The only thing I know that can travel at this altitude is the SR-71 Blackbird. Now it is not uncommon to see high-flying aircraft in this (San Luis) valley, but this guy is calling, in what must have surely seemed like some desperation, on the unsecured 121.5 emergency channel."

"I have two wonderings--was the SR-71 on recon? For what? And why was he so concerned with traffic at an altitude that few pilots have ever been at?"

 (Editor's Comment: The pilot might use the civilian emergency channel if the military frequencies were being jammed. Then again, it might be someone playing with a shortwave radio.)

HUMANOID CONTACT LOS ANGELES, CALIFORNIA

On Wednesday, May 14, 1997, around 4 pm, at the Intersection of Bundy Avenue at Santa Monica Boulevard in Los Angeles, California. (See Journal Entry for May 14, 1997 at 17:00)

TRIANGULAR UFOs OVER RICHMOND, CALIFORNIA

On Thursday, May 15, 1997, at 12:07 a.m… a few hundred yards from Interstate Highway 80.

…a black equilateral triangular object about the size of a half-dollar held at arm's length, moving swiftly to the east-northeast about five degrees north of directly overhead..."It had three lights, one at each of the vertices. These were orange-yellow and appeared as bright as fourth magnitude stars. Each light appeared to be divided into two hemispheres along the axis of motion. The object was moving in the direction of one of the vertices at a high rate of speed. The duration of my sighting was about 4 seconds."

… it passed overhead… It produced no noise except perhaps the faint sound of rushing air… the nearness of the (Interstate 80) freeway makes that impression unreliable.

Twenty hours later…at approximately 10:43 p.m…made visual contact with a UFO.

… a group of lights, perhaps eight or nine clustered near the front edge of a black triangular object with angles of about 120 degrees, 35 degrees and 25 degrees." …. "The object was traveling NE at a high speed with the largest angle in the front and the smallest angle to the NW. … it was about as large as a half-dollar held at arm's length..It passed directly overhead and made no noise, … observed this object for about 6-7 seconds. Its lights were also about fourth magnitude and looked like eyes--almond-shaped with a dark center…It should be mentioned (that) the first object was moving along a flight path out of SFO (San Francisco International Airport) used by passenger craft at high altitude.”

SKY BOOM REPORTED IN MISSOURI ON MAY 15

On Thursday, May 15, 1997, two hours before a "mysterious explosion" rocked southern Ohio and northern Kentucky, a similar blast was experienced in the city of St. Joseph, Missouri (population 76,691), located 54 miles (87 kilometers) north of Kansas City.

A spokeswoman for Offutt Air Force Base in Nebraska, said the blast was "probably a sonic boom caused by an aircraft breaking the sound barrier…that the boom might have been caused by an SR-71 flying from Beale Air Force Base in California to Andrews Air Force Base in Maryland.

Another spokesman for USAF, said "the aircraft would have been in NW Missouri about 2:30 or 3 p.m. on that afternoon.”

BLACK HELICOPTERS IN FRESNO, CALIFORNIA

On Saturday, May 17, 1997…at 10 p.m… two black helicopters in close formation, no sound, no exhaust, and no flashing lights--just a steady white light flew very close to the ground, from the SE to the NW  (Kings Canyon Road to Herndon Avenue-J.T.).

“ Definitely looked like helicopters--but very Stealth-like…they had a wide fuselage, no visible (tail) rotor, could not see underbelly--no visible landing gear. No noise of any type. No exhaust. Both were in tight formation, with one just in front of the other. The one in the rear seemed to be on the right-hand side of the one in the lead.”

On Tuesday, May 20, 1997…the city's ABC-TV affiliate, aired a 15-minute segment on UFOs…showing "a round glowing object."…(prior to the program airing) city residents had been puzzled by reports of black helicopters on patrol over McKinley, Belmont and Olive Avenues, just north of Chandler Airport.

 (Editor's Comment: From the description, the aircraft resemble the new Eurocopter NH-90. But, according to Aviation Week and Space Technology for May 27, 1997, there are only a few prototypes of the NH-90, and all are in Europe. The first NH-90s not expected to be out of production until 2002.)

FLYING TRIANGLE IN CENTRAL PENNSYLVANIA

On Sunday, May 18, 1997, at about 6:30 p.m., a handful of people …at the intersection of Pennsylvania Route 443 and Appleby Road, near Linglestown, Pennsylvania (Pa.) were startled by the appearance of a "flying triangle."

…the UFO was "to the north directly over Route 81.. was …a triangle UFOappearing to be six inches across.

…as to how high the UFO flew… it "was real low" and "moved slowly W."

… "The triangle flew overhead, moving in a WNW direction. The lights gave the appearance of protruding from the actual craft.

… lost sight of the UFO when it dropped toward forest-covered Second Mountain. The sighting took place in a rural section of Linglestown, about seven miles (11 kilometers) north of Harrisburg, the state capital of Pennsylvania.” -- Copyright 1996 - 2012 UFOINFO Editor: Joseph Trainor

The Unfolding

Surah 74 AlMuddathir (الْمُدَّثِّرُ) (The Enveloped/Enfolded/Wrapped Up One)

(74:1) O You Enfolded One (Enveloped/Wrapped Up In Your Mantle)
(74:2) Arise and Warn! (Ascend/Mount Up To Deliver The Message)


You, My Dear, Can give any Message You would like at this point. Since I've been hung out to dry for over 14 years by my reckoning, the only message I feel the need to deliver is in answer to the question, "Why are the planetary orbits elliptical?"

Plane curves (lines, circles, parabolas, sine curves, etc.) that are wrapped onto cylinders of varying radii exhibit a sinusoudal influence, and can be characterised in terms of equations whose solutions are simple 2-Dimensional geometric transformations(rotation, translation, etc.), without resorting to calculus.
A cylinder is a developmental surface it can be 'flattened' or 'unwrapped' onto a plane without distortion--Mathematically expressed as having Zero Guassian Curvature Κ , (intrinsic curvature is Zero). Gaussian curvature is defined as the product of the principal curvatures κ1 and κ2.




Κ = κ1κ2
And since cylinders can be transformed flat without compression or expansion (distortion), unwrapping a curve that lies on the surface of a cylinder preserves the distance between points on that curve. In other words, any arc lengths on their profile unfolds/unwraps/uncurls onto a line segment of the same length. The diagram above shows the simple case where an arc on a right cylinder's circular profile is unwrapped by rolling the cylinder along its side; the end point on the circle projects onto a point t, but unwraps onto a point x. And since the sinusoidal influence is determined by the relationship of the arc length to the linear projection, unwrapping curves that lie along the cylinder surface gives rise to their periodic nature.









By extension, space curves unwrapped from the lateral surface of a right circular cone produce periodic plane curves. (An interesting anolog found in nature of curves unwrapped from conics is the lunar obit).



A line segment (the shortest distance between two points) wrapped onto a right circular cylinder is also a geodesic arc (shortest path) on the cylinder, no matter how tightly it is rolled (decreasing r) and the profile of a geodesic arc on a right circular cylinder is a function of arcsine. * A geodesic on a circular cylinder is always part of a circular Helix.



The profile of such a wrapped line is given by:





p(t)=cr arcsin (t/r) (where; c= constant, r=radius, t= projected point)
In case of a right circular cylinder, eccentricity is 0, where such a line in the xyz plane is given by z=t lies at a 45 degree angle to the generators (a=pi/2), the tightly wrapped line would stack into circular ringlets should the cylinder collapse orthogonally (like a Slinky would when there is no tension). The profile of such a line in this particular case is given by:









p(t)= ct^2





The stacked ringlets (circles) it forms are given by:





z^2 + t^2 = r^2
There are 3 ways to distort these circles into ellipses, by changing the viewing angle either via rotating the cylinder or changing the position of the outside Observer or by deforming the cylinder itself (squeezing it) so that the eccentricity is no longer 0. Changing the viewing angle is simply a matter of shifting perspective (--); physically deforming the right cylinder such that its eccentricity is no longer 0 requires effort (Force).









So, this begs the question, when considering planetary orbits, is it the perspective that makes the orbits appear to be elliptical or something more intrinsic?





From a purely geometric consideration, and realizing that circles are in fact merely ellipses with eccentricity=0, it is strange that the more generic elliptical orbits are the common case and not the perfect circular orbit.





In a 2-body system where a much heavier object is at the center, a circular orbit would be the expected outcome, or the ideal case, in any event. Neptune's largest moon, Triton, comes closest to this ideal case in the Solar system, with eccentricity=0.000016. {That of the Earth's orbit around the Sun is 0.01675 (a far cry from the exaggerated elliptical orbit often depicted in the literature)--based on a cursory look at the limited curricular activity on the web, it's no longer a surprise that the Germans landed first--in my living room--& very good helpers they are, too, even if they do tend to overshop the tomatoes.





The event alluded to happened over a dozen years ago and has nothing to do with my state of mind which was as sound then despite the intractable headache as it is now despite the fact that a casual trip to the local library to pick up a book accompanied by my child has some people conspicuously talking to You about 'stopping her, now!'





Is 'stop her' code for 'shoot her'? (^_~)





And it's a good thing You didn't because it isn't like I don't give You ample opportunities to do just that without the children present; and it would be in exceedingly poor taste if something like that were to happen right in front of their eyes given how much of a predictable, isolated, easy mark I make myself the rest of the time when they are not around.} "<o _<o"





Anyway, back to the present.





That the geodesic is the shortest distance between two points on the surface of a cylinder, regardless how tightly it is rolled up, is interesting from the perspective of an outside observer in that an object or person following this route would appear to be going around in circles (elliptical path), but from that traveller's or object's point of view they think they are travelling in a straight line.





An interesting variation on this theme is if the object or person were to follow a weaving path in a sinusoidal fashion in a plane that is then rolled up into a right cylinder. The sinuous path can represent Time as well as Displacement. One familiar representation of just such a path is the apparent Time Difference due to the Earth's orbit about the Sun (The Time Equation).










A knack for stating the obvious is one of my strong suits. Orbits "unfolded" in such a manner are indistinguishable from displacement due to simple harmonic motion, as found in springs that obey Hooke's Law or the motion of a Pendulum.





In terms of the Geometry, an Orbit is essentially a Straight Line 'Wrapped' around a Developmental Surface (like that of a Cylinder), and its Profile is essentially a Circular (Elliptical) Path.





By extension: Time (t) is a Projection of Orbit onto a Tangential Viewing Plane. Each Point in Time is also a Position (x) in the Orbital path. As that Path (displacement) 'unfolds/unwraps' (theta) onto the Viewing Plane, the Time correlates to a particlular Place (x) on the Orbit's Profile given by:





x= (Time*Theta)/(Sin (Theta))





or x= Time*θ Csc[θ] = ; and





alternatively;











and for the Real Time, and Place and Angular Displacement (Azimuth)











Interstingly has only 1 Real Integer Root at t=0;

Does this mean that In Reality Nothing Really Ever Happens?





(Projecting a Point and/or Unwrapping a Curve from a Developmental Surface is like Stepping Down from a Higher Dimension. When the need to refresh What this is all about arises, we can always go back to How Emily treats Bob, and Where Angels come from--always leaving the residual question, Why?)

"They forgot Y I told U!"
The Argyle Sweater -Confusion at the Alphabet Gang Hideout
Appeared in the March 1, 2014 Los Angeles Times Comics Section

*Unwrapping Curves from Cylinders and Cones, Apostol and Mnatsakanian, 1997, The Mathematical Association of America; pp 392-415

If It Walks Like A Duck And It Talks Like A Duck, It's A Papaya

"It's not the one thing nor the other that leads to madness, but the space in between."
--Jeanette Winterson, Oranges Are Not the Only Fruit

In a nutshell, the cunundrum scrutinized by many-a-sleuth since the Dawn of Civilization has been;
One Duck--But, Which Duck?

Purportedly, the first to pop the question were the Greeks--and it would have sounded something like:
Mia papya amma pya papya?
(Μια πάπια, αλλά ποια πάπια?)...

But, what's any of this to do with Gravity? One might wonder.

In Greek the query whether it is 'One Duck' or 'A Duck' is one and the same. Only interesting as far as 'One' indicates an exact Duck, yet any generic/indefinite duck will do for 'A Duck'.The word for duck in Arabic, by the way is, ' بط' , pronounced 'but' , or more precisely, 'butt'. A closer look at the image of the yellow ducks swimming past the view finder reveals a series of less obvious white ducks gliding by in the opposite direction. They are embedded in the 'negative space' defined by the more apparent yellow ducks.

The white ducks are what we would call a 'ghost' since they have no definite outline. And just like a ghost they trace a faint, weak or greatly reduced appearance, or possibility of something. But, butt, ' بط'...!
...where at first glance it seemed the marksman is about to miss their target, we now see that they are sighting their quarry and are right on target--an interstitial white 'sitting' duck.

In this example, the interstitial space (white ducks) is the gap or 'empty space' between spaces full of structure or matter (yellow ducks). It is what the Japanese call Ma (間) ...roughly translated as "gap", "space", "pause" or as "the space between two structural parts". Now, before you 'O, Ma!' me, or toss another 'grammar nazi' my way (an apparent euphemism for 'childbirth makes women scatterbrained'), You should know the reason I am bringing up the Japanese is not because you have a Japanese girlfriend at present. But, for the more important reason that while this 'interval' or 'negative space' is understood to be experientially 'concrete' in Eastern philosophy, in that its very absence or voidness is considered to lend value to the overall tangible structure or give shape to the whole, there is no equivalent single word for Ma in the English language--a somewhat serious omission.

The buzz words being interstitial and negative space, right? Somehow, that should bring us back down to Earth, so to speak, and the 'matter' under consideration--persnickity Gravity.

For denizens of the Planet Earth, 'Knowing' about Gravity is a little like 'Seeing' a Ghost.

Just like in the Duck example, where the ghostly Ma white ducks were plucked from the negative space or gap between the substantive yellow ducks, Gravity's ghost is traced by the Tide. Oceanic Tides can serve to 'map' Gravity since it has a direct affect on them.

For the example here, a regular ocean tide at the shore gives some insight as to the basic Geometry of Gravitational (wave dual) affects on a particular day at a particular time and particle location.

And just like Flatlanders cannot fully realize what Higher Dimensional objects and forces Really are in Lower Dimensions (Consider Flatlanders, Emily and Bob, projecting a hyper-cube...etc.); the best we can hope for is a reasonable inference of what these 5th, 6th, or higher dimensional things' true nature is based on our limited perspective of what we are afforded by our 3rd or 4th dimensional existence (remember Chicken Little?).

That is to say, we need to look for their traces in the 'empty' spaces.

The sine function, osculating circles, parabolic sand washes and the triangles indicating the carved sand bars were overlayed onto the image by drawing them in, not actually modeling them mathematically. These shapes, while selected intuitively, have geometries that can be explicitly related by arithmetic relationships.

The simplest case is imagining that a cylinder is cut at an oblique angle such that the cross cut is an ellipse. Unwrapping the cylinder reveals a sinusoudal curve. In a similar fashion, the circles, parabolas, and triangles are derived from conic sections and projections (unwrappings/unfoldings). (Implicit formulas for such profiles/projections available at "Unwrapping Curves from Cyliders and Cones," The Mathematical Society of America, 2007 )

Simple inspection of the underlying geometry for this moment in time by the sea shore--the osculating (kissing) circles, parabolic sand washes, the tide's sinuous wave front, and the triangles depicting the carved sand bars-- gives a good lower dimensional representation (affine) of Gravity's extra-dimensionality (interstitial nature) and just what it might Really be all about.

Having spent time mulling over the implications of a mathematically perfect Solar System, as solargeometry eloquently puts it, it would be reasonable to expect infinitely recurring self-similarity throughout the Universe. And, by extension since Gravitation is a part of the Universe, wherever we measure or observe its effects can serve as reasonable isomorphs in our 4-dimensional space-time domain to understanding Gravity's exact nature.

Self-similarity is the flip side of the Duality coin. And just like opposites, or duals, serve to balance each other and teach us something about the Nature of the World by comparing and contrasting these opposites, self-similarity serves as an identity scale from the very big to the very small (You Do It! I simply don't get paid well enough to justify working that hard, http://en.wikipedia.org/wiki/Discrete_Gaussian_kernel#The_discrete_Gaussian_kernel) to teach us about those things that we cannot access readily due to some limitation. In the case of Gravity, that limitation seems to be that it is extra-dimensional.

{It may very well be the case that self-similars do not only exist for inanimate objects, but People as well, considering the Quran has this much to say about them:

نَحْنُ أَعْلَمُ بِمَا يَقُولُونَ إِذْ يَقُولُ أَمْثَلُهُمْ طَرِيقَةً إِن لَّبِثْتُمْ إِلَّا يَوْمًا 20:104

20:104 We know what is involved when the 'likes of them' (those mentioned before, those like them, their representations) say, ‘You went about (were broadcast/remained/stayed/tarried) in this way (method/system/fashion/channel/styling/mode/style/attitude) but a Day'.}

A good place to start looking for self-similars in Gravity's case is by comparing the Curvature of a cylinder to the curl of a Tidal wave.

A cylinder can be given by a flat metric, a 2-D rectangle (planar shape) that is curled (rotated by an angle 'alpha' about its axis) so that the short ends meet. When rotated, its various profiles present as lines, ellipses or circles depending on the viewing angle and axis of rotation.


Curvature characterizes how well Pythagorean’s theorem holds for spatial distances.

A space or space-time with zero curvature is called flat.

If an object/line/field/surface/n-space is ‘flat’ its curvature is zero, then Ω = 1, and Pythagorean’s theorem is valid.

If Ω >1, there is positive curvature (or locally convex), and if Ω <1 then curvature is negative (locally saddle, or hyperbolic--i read it, is it supposed to make me feel any better, or make me launch into a retelling of the story about ذو القرنين ḏū al-qarnayn 'the 2-horned one', as He was already mentioned in earlier posts 'where the 2 (horns?) meet').

In either of these two cases, the Pythagorean Theorem is invalid. The point here being that this type of thing is only detectable on a Cosmic scale (1E26 m); and sometimes that's how big the Truth gets, and they still callin' me a liar! (As an aside, do i get an invitation to the wedding the crew from 'paranoia' were planning at Starbux this morning 02-26-2011 @8:00am? That is to say, the guy on the phone was so loud about it, he should've invited everyone in the joint...I haven't been to one in about 5 years.)

In a plane, curvature is a scalar and in higher dimensions it is described by curvature vectors/tensors.

For a circle, the curvature is equal everywhere, and is defined as the reciprocal of its radius.

For smooth curves, curvature is defined as the curvature of the osculating circle at each point. (Osculating circle based algorithms can also be used to avoid a catastrophe.)


...back to the Sea...

A yellow dot is wrapped onto a cylinder of decreasing radii in the Figure (a)-(f) above.

The edge effect in (f) is reminiscent of waves breaking on the shore.

Pictured here is a yellow dot resting on slack water in an ocean (A), a momentary lull before the tide turns, and something that models a point in a plane (or a Flat field).

In (B) the red arrow indicates an Acceleration field which causes the yellow dot to rise in a trajectory modeled by a geodesic along the surface of a cylinder
(C)--an example of Curvature as the Obstruction to a Flat Field.


 {If You notice how long this post is taking for me to get around to doing it's because I've been sidetracked, thinking I almost made a friend, but that went South quickly when he reminded me that 'human contact is a good thing'. R U kidding?Did you see what happened the last time I came anywhere near them?! So, good try, but no thanks!}

An Observer looking directly down from the Sky  (i.e, a Fixed Point of View, far away) sees the yellow dot translating along a straight line (not following a curved path, since they cannot observe the rotation, α=0, ie. it would appear 'still' in that respect, no longer arcing), its straight line profile traces a path:

p(t)= t


Which is esentially a line given by:

z = ct


The yellow dot's ordinate as it rolls along the curl of a cylinder that's rotating around its central axis in this manner as a function of the angle of rotation about the cylinder's central axis, α, is given by:

zα = p(t cos α +√(r^2- t^2 )sin α

Which is a curve of the form:

zα = t cos α +√(r^2- t^2 )sin α


On rearrangement, is essentially an ellipse (possibly degenerate) of the form

Ax^2 + Bxy + Cy^2 = 1 given by:

zα^2 − 2zαt cos α + t^2 = r ^2 sin^2 α


where:

p = the profile function
t = projection of the point along the x-axis
r = radius of the cylinder
α = angle of rotation about the cylinder central axis
z = the distance the projected point travels parallel to the y- axis as it follows the curl of the cylinder through angle α
(http://www.mamikon.com/USArticles/RollingConesCylinders.pdf)
The expression for zα resembles x'= x cos α + y sin α for changing coordinates from the xy- system to the x'y'-system by rotating the axes through an angle α.

The tidal wave develops along the arcing surface of the imagined cylinder whose shape, depending on the symmetry of the acceleration, may be a circle, an ellipse or degenerate ellipse --an example of Tidal Forces as the Obstruction to an Acceleration Field.

This is readily imagined if one were to change the Observer's point of view, such that they are now sighting directly down the cylinder's central axis. One way to do this is to move the Observer's veiwing plane by 90 degrees by actually repositioning the Observer, the other way to do this is to 'tilt' the cylinder itself by α = π/2 to the original viewing plane.

In either case, the profile function is then given by:

zπ/2 = p(√(r^2- t^2 )

Which is essentially a circle given by:

z^2 = r^2 - t^2

Time and Tide are, respectively, bound to Space and Acceleration akin to the manner in which Polar coordinates are related to Cartesian coordinate systems. The relationship is difficult to fathom directly since information is lost (more accurately, 'masked') when moving from one system to the other. And looking at something (information) in one system makes it seem like something entirely different in the other, when in fact it (the information, representation) is essentially the same exact thing.

Words can only take us so far and that's why pictures were invented. And by the fortunate happenstance of a searchable world wide web, wikipedist Kieff (who for whatever reason does not enjoy being Brazillian, or is that getting a Brazillian?) has actually expressed this concept of converting from Cartesian to Polar coordinates pictorially--a similitude for how Curvature of Space-Time is the same as Tidal Forces."

As for seeing me cycle through every mood but Contrition, when have You ever known me not to oblige. If it's contrition You want, here it is: I am genuinely sorry I didn't kill'em all!}

Good things come to those who wait, or as in this case, to those who procrastinate. The delay in getting on with wrapping and unwrapping (unfolding) curves has allowed enough time for this treatise to surface on the web "Unwrapping Curves from Cylinders and Cones," by Tom M. Apostol and Mamikon A. Mnatsakanian, May 1997, The Mathematics Association of America. (reference added March 28, 2011)

Since it seems Gravity can only be encompassed from a Higher Dimension we can only Infer something about its inherent characteristics by its Lower Dimension isomorphic projection on Tides. In this case, Ocean Tides serve as the 4th dimension space-time model of Gravity’s true Higher Dimensional 'Wave' nature.

The Ocean tides give a direct window into the Wave nature of Gravity since modeling tidal behavior can serve as a reasonable affine in Euclidean Space to Gravity’s n-dimensional space affects on them.As we know Tides vary, Gravity, too, may not be as constant as we think, but also instantaneously variable and fluctuating (just like Energy, Light, and other Electro-magnetic radiation, and we have a basic understanding of how Matter interacts/correlates with such Fields).


Gravity's Wave Duality Can Be Inferred From Geometry of Tidal Affects



The pictures can only do so much because they are still rendered in 2-dimensions but a good modeling program should be able to tease out the Unifying Physics of this phenomenon we call 'Gravity' and the finer points pertaining to fractals, duality, and that niggling issue of 'missing mass' (I mean, if we Know it's missing, doesn't that mean it Ain't?--O, Gee :-() that brings us back to 'There ain't no God'!--i kid, i kid, i jest i jest, b( i am soooo depressed)-er).
Some days, when the tide washes up in even more circular fronts, the effect is even more pronounced.


I'm almost certain some bright talent can put all this "As Above, So Below..." to Music just as some time ago William Blake wrote a Poem about it.


'To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour...

Every night and every morn
Some to misery are born,
Every morn and every night
Some are born to sweet delight...
We are led to believe a lie
When we see not thro' the eye,
Which was born in a night to perish in a night,
When the soul slept in beams of light.
God appears, and God is light,
To those poor souls who dwell in night;
But does a human form display
To those who dwell in realms of day.' --from Auguries of Innocence by William Blake

O, Gee, again! SomeOne already made it down this far in the post and is wondering where is the Quran tie-in. Here it is:
Surah 20 TaHa (طه )

طه 20:1

20:105 وَيَسْأَلُونَكَ عَنِالْجِبَا

فَقُلْ يَنسِفُهَا رَبِّي نَسْفًا فَيَذَرُهَا قَاعًا صَفْصَفًا 20:106

20:107 لَا تَرَى فِيهَا عِوَجًا وَلَا أَمْتًا

20:108يَوْمَئِذٍ يَتَّبِعُونَ الدَّاعِيَ لَا عِوَجَ لَهُ وَخَشَعَت الْأَصْوَاتُ لِلرَّحْمَنِ فَلَا تَسْمَعُ إِلَّا هَمْسًا


The first sign in this chapter is one set of the Disconnected Letters found in certain Chapters of the Quran. They are pronounced individually and generally do not comprise words that have any meaning, for that reason they have kept their integrity all these years.
For Sign 20:1 they are the letters Tta ط and Ha ه .

In a previous post there was some discussion as to the mathematics in the Quran, so going by conventional Arabic math notation the ط can mean 'Natural Number' and/or 'pi' and/or gematria value for tta being '9'. And the Ha is Euler's number which is the irrational number denoted by 'e' and has the gematria value '5'.

Now, it doesn't take much to combine pi and e to come up with a natural number. The general case is:



The general solution for which is:

For the special case when taking the Chapter value 20 as the variable and the Sign number 1 as the case to test for True, we get: 


  

Which happens to be True.


20:105 And they will ask you about the Mountains/Barrows/Highlands; Say, 'My Lord Will blast them (a) demolition (torpedo them (to) sinking)'

20:105 transliteration

Wa ya s a loo n aka AAani al jib ali

fa qu l ya nsifu ha

rabbee nasfan

20:106 Leaving it a level plane (Leaving it bottoming (simply) wasting)
20:106 transliteration

Fa ya فَ يَ

tharuha qaAAan saf safan
 ذَرُهَا (a word for corn/kernel/seed/scatter/sow 'tthura' and here it is understood to mean 'its kernel' since it's take as 'thuruha' (reflexive); but this is by no means the only way it may be understood--just happens to be the most accessible to me.

safsafan

20:107 You will not see in it any Crookedness (Bend/Curvature) or Ruggedness

20:107 transliteration

La ta ra fee ha
(La=no, then use tau, roh, phi, and Ha==e,
should lead to something meaningful
when 20:107 used for variable/solution)

AAiwajanwala amtan

(and not; d, a? Complex, Imaginary, compile/ until n?)
(more than likely the math is wrong since I have no insight into the physics/math and simply stringing along the Arabithmetic guessing, someone more keen on this can probably recognize it for what it is. the point is the message has to do with learning something new and not necessarily using the Quran to bonk your brother.)


20:108 On a Day they will follow the Caller/Summoner, without Crookedness/Dishonestly/Evasion to Him, and the Voices will be Hushed/Overawed by the Merciful, and you'll not hear anything except murmurs/whispers/soughing sound.

20:108 Transliteration

Ya w ma I thi n
ya ttabiAAoona alddaAAiya
la AAiwaja lahu
wakhashaAAati alaswatu lilrrahmani
fala tasmaAAu illa hamsan

Surah 46 Al-Ahqaf ( الْأَحْقَافِ , Curved Sand Dunes)
وَاذْكُرْ أَخَا عَادٍ إِذْ أَنذَرَ قَوْمَهُ بِالْأَحْقَافِ وَقَدْ خَلَتْالنُّذُرُ مِن بَيْنِ يَدَيْهِ
 وَمِنْ خَلْفِهِ أَلَّا تَعْبُدُوا إِلَّا اللَّهَ
إِنِّي أَخَافُ عَلَيْكُمْ عَذَابَ يَوْمٍ عَظِيمٍ 46:21

46:21 And remember 'Aad's bretheren when He warned his people among the wind-Curved Sand Dunes, and indeed warners came and went before and after him, saying: 'Serve none but God. Truly, I fear for you the suffering of a Momentous/Significant/Great/Extraordinary Day'.

But like I stated earlier, it's taking time to get through this post since I tend to wallow in my own misfortune, knowing this News never makes it Home (with or without outside assistance, given how often the point about hyperbolic curvature has been deleted to date 21/02/2011; the upside is that while so far Gravity is still present I have magically dropped 3 dress sizes while still consuming the same amount of chocolate). {'Grammar Nazi'?! Really? How many more times You gonna say that?}