Phunny Physics Take II

While Newton's laws are adequate to describe the motion of an idealized object's motion in an inertial frame they proved inadequate to characterize the motion of rigid bodies and deformable bodies, necessitating the development of more generalized laws of motion for rigid bodies by Euler based on Newton's groundwork.

If a body is represented as a continuum of discrete particles, each governed by Newton’s laws of motion, then Euler’s laws can be derived from Newton’s initial concepts.

Likewise, while Newtonian mechanics is a useful approximation for objects moving at speeds much slower than the speed light, for moving frames of reference and objects moving at faster speeds, it has been superseded by Einstien's Special Relativity; and for objects on the atomic scale Einstien's General Relativity and quantum mechanics provide the better heuristics.

This is not to say that Newton's ideas which first appeared in his Philosophiæ Naturalis Principia Mathematica in 1687 (along with the Calculus) were wrong, as they served to successfully describe and predict planetary motions and the orbits of thier satellites, and provided the basis for the more accurate and comprehensive theories that were predicated on his initial concepts, but that they were nascent.

Newtonian mechanics served as the precursor to the more highly developed ideas fostered just by his having proposed them in the first place.

{He Said, "Can you write it so a kindergartner can understand it?"
I was not aware that was my audience, but here goes, "In Life You Are what You Eat, and in Death it's what You've Read."}

With this in mind and mayhaps a little tongue-in-cheek, this blog entry serves as a convenient cross-reference between more familiar verbage and concepts we come across in our common experience and what A Page In The Life tries to tease out from the Quran as Knowledge Object.

Familiar Concepts from Douglas Adams

-- Arthur after his first ever teleport ride.

"`You know,' said Arthur, `it's at times like this, when I'm trapped in a Vogon airlock with a man from Betelgeuse, and about to die from asphyxiation in deepspace that I really wish I'd listened to what my mother told me when I was young.'
`Why, what did she tell you?'
`I don't know, I didn't listen.'"

-- Zaphod.

"`If there's anything more important than my ego around, I want it caught and shot now.'"

-- Zaphod.

"`Hey this is terrific!' Zaphod said. `Someone down there is trying to kill us!'
`Terrific,' said Arthur.
`But don't you see what this means?'
`Yes. We are going to die.'
`Yes, but apart from that.'
`APART from that?'
`It means we must be on to something!'
`How soon can we get off it?'"

-- Evidence that there will be some justice in the Universe eventually.

"`She hit me on the head with the rock again.'
`I think I can confirm that that was my daughter.'
`Sweet kid.'
`You have to get to know her,' said Arthur.
`She eases up does she? '
`No,' said Arthur, `but you get a better sense of when to duck.'"
-- Ford and Arthur on Random.
Dirk Gently's Holistic Detective Agency

...and from Funny Phrases

According to my best of my recollection, I don'tremember.

If you cannot convince them, confuse them.

Don't take me literally.

Tomorrow will be canceled due to lack of interest.

Sex is not the answer. Sex is the question.Yes is the answer.

The more things change, the more they stay insane.

You cannot achieve the impossible without attempting the absurd.

I have always been crazy, but it kept me from going insane.

I have crossed and recrossed the line between sanity and madness so many times that I have all but rubbed it out.

Around here, to be nuts is normal, to be sane is stupid.

Reality is a figment of your imagination.

It's not just reality that matters.

Avoid reality at all costs.

Imagination is the foundation of reality.

Where does it go? It doesn't matter. Flush it.

No matter where you go; you're there.

Gravity is a myth, the Earth sucks.

Abandon the search for Truth; settle for a good fantasy.

You can't dream too much; you can't do enough to make your dreams come true.

If all else fails, throw up.

If you understand something today, it must be obsolete.

It's only hopeless if you walk away.

Life is a glitch in the universal program; death is just the programmer's way of debugging.

Death is life's way of telling you you're fired.

Death is the consequence of being alive.

Clever is getting out alive.

Don't worry about life; you're not going to survive it, anyway.

It's all a pigment of your hallucination.

In theory, everything works.

Plagiarism is copying from one source; research is copying from two or more.

People who think they know what they're doing are especially annoying to those of us who do.

More Familiar Concepts from Douglas Adams Quotes

Quick!! Act as if nothing has happened!
"He believed in a door. He must find that door. The door was the way to... to...
The Door was The Way."
"Good.
Capital letters were always the best way of dealing with things you didn't have a good answer to."
-- The Electric Monk discovering the reason why there are so many acronyms in computing.

"He had extracted himself from the Cambridge one-way system by the usual method, which involved going round and round it faster and faster until he achieved a sort of escape velocity and flew off at 
a tangent in a random direction."
-- Quantum transport physics explained.

Could we perhaps take a snakebite detector with us to Komodo?'
`Course you can, course you can. Take as many as you like. Won't do you a blind bit of good because they're only for Australian snakes.'
`So what do we do if we get bitten by something deadly, then?'
He blinked at me as if I was stupid.
`Well what do you think you do?' he said. `You die of course. That's what deadly means.'"
-- DNA failing to spot the obvious.

"`You're proposing twenty hours on a boat...'
`A small boat,' added Mark.
`On violently heaving seas...'
`Probably.'
`With a three-day-old dead goat.'
`Yes.'
`I hardly know what to say.'"

-- DNA learning what fun awaits him on the way to Komodo.

"He stood up straight and looked the world squarely in the fields and hills. To add weight to his words he stuck the rabbit bone in his hair. He spread his arms out wide. `I will go mad!' he announced."
-- Arthur discovering a way of coping with life on Prehistoric Earth.

Paul Revere was a tattle-tail.

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?!')

Talk Like An Egyptian

You know how I know You are wayyy too late?
Because it's come to this and I still don't see anybody around here that I recognize (I thought I did, but he denied it, then deleted any info on the web that pointed to it).


So, for this part, I am guessing I have to talk like an Egyptian.

The old song goes:
العتبة قزاز
والسلم نايلو ف نايلو
The Step (Threshold) is Glass
And the Ladder (Stairway) is Nylon, Nylon...

Surah 24 An.Noor The Lightاللَّهُ نُورُ السَّمَاوَاتِ وَالْأَرْضِ مَثَلُ نُورِهِ كَمِشْكَاةٍ فِيهَا مِصْبَاحٌ الْمِصْبَاحُ فِي زُجَاجَةٍ الزُّجَاجَةُ كَأَنَّهَا كَوْكَبٌ دُرِّيٌّ يُوقَدُ مِن شَجَرَةٍ مُّبَارَكَةٍ زَيْتُونِةٍ لَّا شَرْقِيَّةٍ وَلَا غَرْبِيَّةٍ يَكَادُ زَيْتُهَا يُضِيءُ وَلَوْ لَمْ تَمْسَسْهُ نَارٌ نُّورٌ عَلَى نُورٍ يَهْدِي اللَّهُ لِنُورِهِ مَن يَشَاء وَيَضْرِبُ اللَّهُ الْأَمْثَالَ لِلنَّاسِ وَاللَّهُ بِكُلِّ شَيْءٍ عَلِيمٌ (24:35

The standard word for Glass (zujajatin) زُجَاجَةٍ appears in the Quran Chapter 24 and is discussed in an earlier post The Chair and The Lamp
Other mentions of glass or cups/chalise occur in the following verses:

Surah 27 Al.Naml Ants
قِيلَ لَهَا ادْخُلِي الصَّرْحَ فَلَمَّا رَأَتْهُ حَسِبَتْهُ لُجَّةً وَكَشَفَتْ عَن سَاقَيْهَا قَالَ إِنَّهُ صَرْحٌ مُّمَرَّدٌ مِّن قَوَارِيرَ قَالَتْ رَبِّ إِنِّي ظَلَمْتُ نَفْسِي وَأَسْلَمْتُ مَعَ سُلَيْمَانَ لِلَّهِ رَبِّ الْعَالَمِينَ 27:44 

Contextual Interpretation
27:44 He (Solomon) said to Her (She'ba), "Enter the Castle/Tower!" Yet when She saw it, She deemed it 'a deep watery expanse' and She bared Her legs (so as to wade into/across it). He said, "It is a Caste/Tower made of (paved with) glass." She said, "O, My God! Indeed I have 'wronged myself,' and She surrendered (became a Muslim) as Solomon had to God, the Sustainer of All the Worlds.


Inni Atthlumtu nafsi     إِنِّي ظَلَمْتُ نَفْسِي   is typically understood to mean that She'ba had sinned against herself, which may or may not be the essential meaning of the phrase and I kind o' know how this could be misconstrued.

Based on first hand experience, whenever 'He' comes out of 'nowhere' and tries to show someone an 'alternate route' so they don't get stuck in traffic, 'He' doesn't exactly announce 'Himself' by 'Name.'  What I actually 'heard' Him Project was 'It's Me!' And I quickly got out of the way and allowed Him to Pass me (see, me with a lower case m, not Me!, like that.)

So, if She'ba had a similar encounter, She had no other way to refer to Him other than 'Me', which anyone not having had the experience would mistake Her for referring to Herself when in fact She had no other way to talk about Him other than that He Referred to Himself in the First Person Object Pronoun 'Me' when She'ba 'heard' Him, too.

And She'ba, having attracted Solomon on a level where She scored an invitation to His digs, probably was not a woman prone to 'tthulm'  ظَلَمْ ,as in sinning or wronging Herself or others, (else He would have met Her on the Battlefield), but that She probably Had 'passed' or 'eclipsed' or 'shadowed' Him (Who?, Why, Me, of course!). How's that for Hilarity? (Note to Solomon,; don't worry Your handsome self about it, I am not asking for an invitation to Your House, since I know you are Married to Her, and I don't want to invite such bad karma as putting designs on some other woman's man--it's like I been telling every One all along, Yous got the wrong girl!)

But for the pragmatic, pedantic, application to electronics and antennas, say, We go with this one--

27:44 So, He (Solomon) said to Her (The Queen of Sheba), "Enter/(Log In)/State/Bring Down/Cut Open/Profess/Say/Affirm 'True of False' the Palace/Tower/Edifice/Story," and upon seeing it She thought/deemed/calculated/estimated/cast==threw across/cipher==put into code/computed (it) a pool of water, (an) Abyss/free space/indefinite expanse/immeasurable deep, fathomless cavity or expanse and She uncovered/revealed/showed her legs/trunk/crus/drive(s)/var. reddish-brown clay; He said/declared, "(It's an) Edifice/Palace/Tower/Story Paved/Satellite?/Tiled/Covered/Surfaced/Protected (aisle/pathway/lane supported (Disciple) from/of Glass/Bottles/Warrior Forces===Competing Forces/Fighting Forces." She said, "My God (Sustainer/Supporter/Creator)! I've been wronging/lost/shadowing/shading/umbraged/ghosting/lie-ing to myself and I surrender/believe, as with Solomon , God (Allah) Is The Sustainer/Creator/Supporter (of) The Worlds!"

According to 27:44, Sheba plays it straight and immediately Repents when She figures out that She'd made a mistake believing what She sees as a bottomless pit or a pool of water is nothing more than the shiny glass tile floor of Solomon's Palace. Because She had not seen anything like it in Her worldly experience she interpreted something unknown to Her, in this case the glass floor, as something She could understand, a pool of water--and immediately understood that Her limited Worldly experience kept Her from understanding the Greater Reality (The Unknown).

This anecdote would lead Any one of us to empathize with Her, not because She was a 'sinner', but because it is a Human frailty that we cannot immediately grasp the meaning of a new concept (an experience alien to our Life's experience) without some familiar point of reference, which may lead us to draw a wrong conclusion. For Sheba, her misinterpretation made her bare her legs to wade into what she thought was the water, for Me it means making one math (physics, spelling) mystake after another! (Besides, Solomon made it really easy for Sheba by offering an explanation on the spot AND making Himself available to witness Her surrender (Islam), unlike my case, where after a 19 year Hazing, the 'twin paradox' I run into denies it so to Whom should I surrender? Given the further razzing that someone surfs into this site with the search phrases, 'surrender fuzzy one,' and 'furj tired,'  and the winniningest one , 'I'm too cute too be obtuse'; besides, I'm a Muslim in the first place, is there such a thing as a double surrender? In that case, make mine a Double! Where do I go with that information, the nearest police station?)

At any rate, the basic understanding is that Sheba miscalculated the 'free space', that it was either boundless and/or had some other property having to do with or exclusive of 'reddish brown' clay, which leads me to thinking it having to do with diatomaceous earth??; (applications in nanotech, vacuum insulation, thermal barrier, can be selected or synthesized for color (distance between planes of regular packed spheres approx. 1/2 wavelength of the visible light...//waveguides) 

Unlike Her, I show no sign of Repentence, because I know this is what passes for Comic Relief around these here parts. And will add to my embarrassment by flagrantly conceptualizing 'Solomon's Palace,' given my keen inaccessible insight into the Unknown, relying heavily on the premise that it should work on some level (As Above, So Below!).

Okay, I lied, and I'm not building Solomon's Palace, for one thing who needs that much housework--I'm going for the Tower! (He Says, "And for another, what's the use when She picks up the land under it and slings it across the room like Sunday night's hash from Mel's Diner."--so, I take it that was not Holy Water they sprinkled me with for that little creative bent?)

Solomon's Tower So Far...See The Ladder?

Diamataceous Earth Puzzle Jar by Candalaria
(Nothing Says the Tower cannot Resemble This
But We R Being Cone Heads Here)

Key Design Parameters:
c= the full length of the 'ladder' which forms the side of the conic (the generators);
(it's fun when my readers offer to help, One surfs in with the search phrase, 'a man climbing the stairs is doing work against gravity,'  as when a Painter climbs a ladder, yet He Insists He is Not a Painter, but a ;Producer! And I say, 'So, You're the One that Produced this mess?' The while thinking, 'I am so tired of this walk-through as every Jim Carey movie character--that's what happens when the ;Producer refuses to listen to the Writer--ideas get stale fast!')
h= the height from the top of the 'tower' to the base of the cone
a= the vertex angle, or the angle of incline of the ladder/lattice to the vertical (approximately 15º)
r= is the..., (about one-fourth the ladder height, c ; ie, minimum r ==(1/4)c)
-Each step/rung of the ladder forms equally-spaced, even geodesics around the conic surface
-The ladder/lattice rails form (Lie along) the conic generator(s)-Depending on which portion of the electromagnetic spectrum is being propagated, the cone may either be a solid surface(conductive or dielectric) or open structure (free space) surrounding a tube or solid core (conductive of dielectric). If the latter, the clearance between the back of the ladder/lattice and anything behind it is at least...
-The top of the ladder/lattice structure must overextend the top rung/geodesic/conic 'landing' by...
The allusion to the 'Tower' being an Ediface of 'Bottle/Glass' seems to indicate that the dielectric (threshold/doorway) is borosilicate glass or the type of glass typically used in making bottles (Schott glass) or maybe drinking cups (soda-lime glass), vs. silica (like  fuzed quartz that's used in fiberoptics; counterintuitive, but that's what this says.)

The further allusion to being 'Competing Forces' indicates that relationship between the signals? similar to when 2 or more actuators provide conflicting inputs to a mechanism, that Sheba 'bared' her legs in order to 'step in' or 'enter' reinforces the imagery in that Human legs are another example of 'competing actuators'. Actuators is broadly described as any type of controller or system that converts one type of energy into motion, serving as the mechanism by which an artificial intelligence or autonomous being (ie, Human) acts upon its environment. 

That Solomon's Tower, described in Sign 27:44 as a  signal tower/ediface/satellite? is some type of antenna is further inferred from the language pertaining to 'competing forces,' typically associated with actuators (an antenna being a special case of an actuator that converts Radio Waves into Electric Energy (EMF) and vice versa).

Surah 76 Al.Insan Human
وَيُطَافُ عَلَيْهِم بِآنِيَةٍ مِّن فِضَّةٍ وَأَكْوَابٍ كَانَتْ قَوَارِيرَا 76:15
قَوَارِيرَ مِن فِضَّةٍ قَدَّرُوهَا تَقْدِيرًا 76:16


The word قَوَارِير kwareer is understood to mean glass/cups/crystal in another 3 verses. In 27:44, Solomon describes the floor of His palace as being صَرْحٌ مُّمَرَّدٌ مِّن قَوَارِيرَ , where the word qwareer قَوَارِيرَ is used to describe the surface and generally interpreted as 'glass.' In 76:15 denizens of Paradise are given cups قَوَارِيرَ made of glass or crystal, أَكْوَابٍ كَانَتْ قَوَارِيرَا and in 76:16 the cups or crystal are described further as being made of Silver قَوَارِيرَ مِن فِضَّةٍ which the recipients themselves determine or establish the measure/value of (typically assumed to be set by their own good deeds).



Tower/Ladder Analogy Sun/Earth/Mars Solar Geometry


Further description of the floor of Solomon's Tower.  صَرْحٌ مُّمَرَّدٌ مِّن قَوَارِيرَ  sarhu mammrrad min quwareer

صَرْحٌ sarhu v. clarify, say, profess, declare, bring down, cut open; n. tower, palace, edifice;

مريد:  n. supporter/satellite; adj. 'big with child' (ie., every process, (except process 0), has one parent process (caller), but can have many child processes(callees))--the understanding here is that the process calls 1 'big child' (ie. significant/immense/huge production/outcome/result/descendent/flow).

ممر n. passageway, corridor, path, aisle, lane, gangway


مرد  due (owing, fitting, right and proper, correct, appropriate, exactly, straight, expected, payable)

رد  n. response, reply, rejoinder, reprecussion; v. reply, answer, repay, counter, repulse, rebound, reverberate, drive back, spurn, disallow; adj. becoming

_{I really don't understand why You censured me earlier today when attempting to put all this together (>_<)_is it meant to channel a gamma ray burst or a Solar flare?}

Earworms and Talking Heads, An Accessible Simile to Time

Letting the days go by, let the water hold me down
Letting the days go by, water flowing underground
Into the blue again, after the money's gone
Once in a Lifetime, water flowing underground
same as it ever was, same as it ever was, same as it ever was, same as it ever was
Same as it ever was, same as it ever was, same as it ever was, same as it ever was
--From Talking Heads' Once In a Lifetime, Lyrics by Keith Urban

The Quran encourages us to reflect on natural phenomena in order to conceptualize God without the ability to make a direct observation of 'God' while we are alive, since just like envisioning a hyperdimensional object in a lower dimension it is near impossible to phathom an Infinite Being when we are limited by the 4-Dimensional Spacetime we are born into.

In 'A Gardner Like That One,' following the geometry of how spacetime evolves from 'spin foam' led to the conclusion that Time does not exist near the Planck scale, that it is discontinous and changes abruptly from one tick to the next.

While the observation and the math is correct, the analysis is skewed by the fact that Time's apparent disappearance is akin to 'water flowing underground' (an allusion is made to this effect in Sign 6:6, Time/like water flowing beneath them like a River) where we can't directly observe it, rather than its popping into and out of existence. The conclusion that something (Time in this case) goes to Nothing and then emerges from Nothing just doesn't make any sense (ie., that Information is Lost then Wanders back out of the Void, with the memory to pick up where it left off?).

The apparent discontinuity may better be explained if we look for an accessible similitude (As Above, So Below), the same way we can intuitively comprehend an Infinite Being (God) with our limited Human faculties, Time can be understood in a similar fashion as we observe the Earth's Water Cycle. Actually, the Water Cycle is mentioned quite often throughout the Quran, and Time is alluded to as flowing like a River (the homonym Days/Time/River).

PS Before I forget:
He Says: The Smartest Thing I Ever Did My Whole Life Was Never To Say A Word To That Girl.
She Says: That's Why Telepathy Was Invented, Dear.

Tesla Girls, Tesla Coils, She's My Tesla Goy-Um!

But Siriusly, an idea that is ahead of its Time is about as popular as the one that goes against the accepted Tide, relegating its proponent to Loopy (Round-the-Bend) status--without further introduction, I give You, Tesla!

"I hold that space cannot be curved, for the simple reason that it can have no
properties. It might as well be said that God has properties. He has not, but
only attributes and these are of our own making. Of properties we can only speak
when dealing with matter filling the space. To say that in the presence of large
bodies space becomes curved is equivalent to stating that something can act upon
nothing. I, for one, refuse to subscribe to such a view."
--Nikola Tesla
(1856-1943)

Tesla's adamant refusal to adopt the little understood yet highly regarded (then as now) views of the vanguard of his day, put him instead in league with the 'luna-tics', aka Renaissance Thinkers and Prophets, or just your run-of-the-neighborhood crazy mother.

While there is no denying that both the Theory of General & Special Relativity do a serviceable job in explaining and even predicting certain phenomena, the very fact that the one necessitates the other hints that they each are incomplete which begs for careful vetting.

And while my undistinguished career is a dim bulb compared to either Tesla's or Einstein's resplendent contributions to Science, it hasn't escaped me that Tesla may have had a real concern with Einstien's Relativity and may not have been simply casting aspersions. It may very well be the case that space itself is not 'curved' due to the presence of matter (heavy objects) since what we are observing/experiencing is a 'projection' of the True Nature of the Matter under discussion.

By 'projection' I am not refering to our simplistic view of holograms, which may serve as a good analogy, but something much deeper than that. Some 'other' physical entity that due to its extra-dimensionality (hyper-space, or whatever the common catch-phrase-of-the-day is), we cannot gauge directly but should be able to deduce its presence much the same way similes, metaphors, and music can convey something as indeterminate as what someone else is feeling without our having to sense it ourselves.

The limited 4D space-time only allows us rare glimses into the larger picture. It's a little like looking out of the porthole (A Gardner Like That One above) of an ocean-going vessel and thinking that's all there is to the ocean. Enough wrangling with the words, time for the GeoMetry (gee, i'm a tree!) using a concrete example.

{And to our left, allow me to call Your attention to the Bliss comic panel of Tuesday May 17, 2011, insinuating that a b**tch explains 'it'; an accolade meaning "Congratulations! __ (Insert Name) has now graduated UFO Academy (summa cum laude)"}
The orbit of the Moon around the Sun is a convex curve approximated by:
(400cos t + cos 13t, 400 sin t + sin 13t)

When expanded this yields:
160000 cos^2(t)+cos^2(13 t)+800 cos(13 t) cos(t)
+ 160000 sin^2(t)+sin^2(13 t)+800 sin(13 t) sin(t)

Which can then be simplified to: 160000 + 800 cos (12t)

And since we're not trying to land anyone on the Sun or the Moon, but simply doing this as an excercise to bridge the esoteric to the familiar, we can say the relationship approximates:

160000 + 800 cos (13t)
or about 40 + cos (13 t)

And, thanks to wolframalpha, the (exagerrated) curve for which appears on the right.

A few things worth mentioning about the Moon's orbit around the Sun is that it is essentially elliptical, it is locally convex, and when we consider the sidereal month of 27.32 days instead of the synodic month of 29.54 days, the ellipsoid is more like a tridecagon.

From studying the concept of 'unwrapping' curves from developmental surfaces, we learned a curve that lies on a conic surface and its ceiling projection are the same type, such that an ellipse projects as an ellipse, a parabola projects as a parabola, and a hyperbola projects as a hyperbola; although, their eccentricity may differ. And we know from observation that the radius vector (r) of objects with elliptical orbits 'sweeps equal areas in equal times'.

That last statement about elliptical orbits is how we were taught to think about orbits in school. Thinking in terms of 'uwrapping' and/or 'projecting' curves from developmental surfaces (such as cylinders and cones) simplifies this relationship since the areas are preserved in much the same way arclength is invariant, eliminating the need to consider the Time, and allowing us to focus on the spacial attributes alone.

{Proofs and more illustrations can be found at the source used here, "Unwrapping Curves from Cylinders and Cones," by Apostol & Mnatsakanian (The Mathematical Association of America, Monthly 114).}

The illustration on the left depicts a conic curve C with its 'ceiling projection' curve C0 (A ceiling projection of a conic curve is like having it lie on the surface of the cone and then the cone is 'popped' open like one would an umbrella). Conic curves projected in this manner have the following attributes:

1. a focus at the Vertex of the cone
2. a directrix L at a line of intersection of the cutting plane and the ceiling plane
3. eccentricity denoted by lambda = tan (alpha) tan (beta)
4. is a polar equation:


r (phi) = r(0)/(1+ lambda*sin(phi))


Having one focus at the vertex of the cone is significant in that we know for elliptical orbits the center of mass of "...the orbiting-orbited system is at one focus of both orbits" and the general assumption is that there is "... nothing present at the other focus."


However, in the search for 'missing mass', based on conic projections of orbits and the relationships between the viewing plane and the observed point P0, and what we know of the observable 'detectable mass', it would be safe to posit that the second focus is actually the barycenter of the 'missing mass' related to P0 ( which in Reality is a projection of the Actual point P; while it cannot be observed directly from the viewing plane, however, its 'gravitational' effects probably are what manifest as the presence of the secondary focus, which makes it appear as if 'there is nothing present at the other focus').

Conic C (figure above left) and its ceiling projection Co share the following relationships:

1. the ratio of the projected curve
Co radial vector (r) to the distance (d) is constant and independent of
P or Po and is the same as eccentricity (lambda) s.t. r/d = lambda = tan
(alpha) tan (beta)

2. the polar equations
of the unwrapped curve (C) and its ceiling projection (Co) are related by a
constant k = 1/sin(alpha) s.t. R(theta) = k r(theta)

3. the area A of the projected curve Co after one complete
revolution (phi =2 pi) of unwrapping the curve C is given by:

A = E cos (beta) = S sin(alpha)= pi*rho*s

(where: E= disk area of conic C, beta = its angle of inclination, S= finite lateral surface of the cone subtended by C and its vertex, alpha = the half-angle of the cone with vertex angle=2(alpha), rho = radius of the cone base, s= unwrapped arclength of C on the surface of the cone.

A generalized conic is a planar curve generated when a conic curve is projected onto a ceiling plane with a focus at the vertex (V) of the cone. In the figure above a generalized ellipse with period interval length 2pi/k, k=5.5, lambda = 0.22 is generated after 1 period only. In (b) and (c) the same generalized ellipse after 5 and 11 periods, respectively.
The figure on the right depicts an approximate annual orbit of the Moon around the Sun as a generalized conic; 1-year orbit is about 13 synodic months, or 13 periods.

According to the figure on the right the period interval length is approximately
55.4 deg =2 pi/k,
giving
k=6.5

Similar shapes found in nature may be describe in the same manner.

{having run my one brain cell to the ground getting this far, time to move on to a refresher exercise otherwise known as "physics from lyrics"} And, yes, while the aim of all the above may seem nebulous, that's more owing to lack of time than understanding on my part, and the fuzziness clears right up given a little attention. A little like when expressing the simple sentiment "all roads lead to Rome" as a refomulated old Irish Blessing, "May all roads lead You Home", which could prove to be a Curse as much as a Blessing, depending on who You find waiting there for You.

The main idea is to derive the orbit as a generalized conic and consider that there is symmetry in the integral of a smooth function f over the closed boundary of a geometric curve S that is equal to the integral of the derivative of the function f ' over the figure S itself. {What she said, expressed succinctly in the equation below, and That's why Math!}


The explicit form of this relationship appears in physics time and again. The linear case as the Riemann integral (calculating the function at the endpoints of a line equals the integral of its derivative on the line); the 2-D case of integrating f over the closed curve bounding a surface equals the integral of f’ on the surface (as in Stokes’ Theorem and Ampere’s Law); the 3-D case as given by Gauss’s Law of integrating a function f over a closed surface surrounding a volume equals the integral of f’ throughout the volume. (from THE MAP OF PHYSICS, EXPLORATIONS OF NEORATIONALISM, Essays in the Nature and Uses of Reason, by Dennis Anthony)

Ceiling projections of a hole drilled (bored) through a cone’s axis.
Compare to Cassini Ovals, below.

Bean Curves, Qurartic Curves have Parametric Given By:

Ceiling projections of a hole drilled (bored) through a cone’s axis. Note: Bean Curves appear in the first column bottom row, (from Unwrapping Curves...)

Cassini Ovals, Quartic Curves Given By The Parametric

{I am no apologist, but You know by now that I pretty much forgot much of my key life experiences up to this point, especially the higher-learning part of it, but it seems I can finagle some understanding of it up to 9th grade (which includes Geometry & Trig). (And, don't be misled into thinking or trying to figure out this weird amnesia; that, while it may seem to be selective, at times I think it is a protection mechanism and at other times it may serve as the only polite way to avoid having to confront the outlandish; especially when random strangers 'say' things about me like 'why can't she remember' in the third person while they stare pointedly at me and know I am present. Since I don't know who 'they' are and none of them seem to ever bother with an introduction, I act like I don't 'hear' a thing--so, go right on talking about me to me like I am not in the room!) }

I am constantly reminded that 'it' is not about Me, and my Ego is not so grandiose nor so fragile as not to permit continuing to operate under such an assumption--that it isn't about Me. Can You imagine how paranoid I would be if I ever thought it otherwise, especially when confronted with song lyrics about "Every Breath You Take" (The Police).

So, let's just say, for argument's sake, that it is about Sting (the talent behind the aforementioned lyrics) and what Sting may have been thinking when he wrote the lyrics to "Ghost Story".

Since Sting is an Englishman by birth and speaks English as his first language and was an English teacher, it may be reasonable to assume that he means what he says and says what he means (in English)--making him one of the most literate songsters around--making his lyrics relatively easy to parse for our purposes here.

What is the force that binds the stars
I wore this mask to hide my scars
What is the power that pulls the tide
I never could find a place to hide

What moves the Earth around the Sun
What could I do but run and run and run... -excerpt from " Ghost Story" lyrics by Sting from the album "Brand New Day"

While the lyrics are profound and the experience of hearing Sting's rendition of "Ghost Story" quite moving, the answer to many of his questions is "I don't know." At the end of the song, the listener is satisfied with Sting's jump to conclusion, "I must have loved you."

Really? Is that all? Just an assertion without any proof? Just a series of observations and a lack of post doctorate studies in physics or math?

To demonstrate how well this model runs without Me, I will now show (Computer Command Copy on Write) that Sting unwittingly holds the answers to his own thoughtful questions. (Not by Magic, but by the premise that All Inspiration comes from God--that's why You should just tell me and not have to rouse Mr. Sting up from his sound slumber in the middle of the night to go multi-platinum with it.)


W/hat is= the force F, that binds the stars (Gravitational Binding Energy)...
Ŵ=∫▒〖F dx〗; Ŵ=BE ; F = dŴ/x+c= dBE/x+c



W/hat is= the P(power), that pulls(mechanical work) the tide (tidal)


W/hat moves(equation of motion for) the Earth around (polar/cylindrical/orbit) the Sun

W/hat could I(Current, Impedence, Impulse) do but run + run + run (streaming) (you could take a walk)

W in physics/math can mean a few things directly applicable to the query:

W= watt (unit of Power); W= mechanical Work; W= dimensional (w(width) or ωx (frequency); W=Lambert W function; W = W Boson.


Just a cursory look at the lyrics indicates that they break down the physics in somewhat of a coherent way, in that Work is the amount of energy transferred by a force acting through a distance in the direction (vector) of the force. The units for Work and Energy are the same (joules), scalar quantities, and Watts are units of Power which is the amount of energy expended or work done per unit time (dW/dt)--a differential.

Sting's veiled, yet keen, insight is more evident when W is understood to be the Lambert Function, which provides an exact solution to the quantum-mechanical double-well Dirac delta function model which consists of a time-independent Schrödinger equation for a particle in a potential well defined in one dimension. Applications of the Lambert W function is ubiquitous in physics including, but not limited to, the areas of atomic, molecular, and optical physics.

And while W as width may seem out of place with the other W indicators, it makes perfect sense in this context when considering Feynman's assertion, and it seems only appropriate that Feynman be mentioned along with Tesla and Einstein:

• "These notions of potential and kinetic energy depend on a notion of lengthscale. For example, one can speak of macroscopic potential and kinetic energy,
  which do not include thermal potential and kinetic energy. Also what is called
  chemical potential energy (below) is a macroscopic notion, and closer
  examination shows that it is really the sum of the potential and kinetic energy
  on the atomic and subatomic scale. Similar remarks apply to nuclear "potential"
  energy and most other forms of energy. This dependence on length scale is
  non-problematic if the various length scales are decoupled, as is often the case
  ... but confusion can arise when different length scales are coupled, for
  instance when friction converts macroscopic work into microscopic thermal
  energy."--Feynman

Feynman specifies "length" but the general meaning is a scale of 1-dimension, so, length, width, height, etc. are exchangeable. Of course, what Feynman is really talking about, in physics parlance, is the idea of fractals "As Above, So Below."

The /hat (^ ) operator, usually presented over a value or function means: Fourier transform; the element removed from a set; a unit vector (a dimensionless vector with magnitude 1); or used to denote an estimator or an estimated value x vs theoretical x. Read as x-hat or x-roof, where x represents the character under the hat.

Given the various interpretations of W above, the implications are:

• since Work, Energy, and Power are scalar in our 4D space-time, in order for them to be understood as vectors, they must be moved up a notch (or 2 or more) in order for w/hat to make sense as a unit vector (dimensionally speaking); so, based on the 'lyrics to physics' these relationships hold true in higher order dimensions as non-scalars. {So w/hat if I'm wrong? The Theory Of Everything must include Everything from A Tree Grows in Brooklyn to the Kitchen Sink!}
  
  ..look, a joke can run its course and in this case been taken too far, but I have to say hearing "the wife" reference coming from strangers is offensive to say the least and utterly ignorant & insensitive to put it mildly.{I need to see my Father, stop paying bills & stop getting e-mails at the office from colleagues who verify my e-mail address is not ever in their send log}