Word Problems

If you take the time to plow through this blog, you may become convinced that there are several different ways to see or understand the same exact thing; not simply due to different view points (remember Bob and Emily?), but because it is the Way in which the Message propagates throughout the multiple levels of Reality.

But preferring not to deal with esoteric arguments, there are concrete examples of how this multifaceted approach works in our everyday (collective) life.
A specific case in point would be how we think of the Moon and its orbit around the Sun. I found a good discussion about this at The Orbit of the Moon Around the Sun is Convex! , and it serves as a good example for this post about Word Problems.

Summarily, there are some who believe the Moon’s orbit around the Sun is loopy, having negative curvature at times, and others who think it traces some elliptical or circular path, when in fact (in a 3 or 4 dimensional context) it approximates a convex polygon with rounded corners.
Based on a sidereal month the polygon would have about 13 ‘corners’ since 365.25 days to orbit the Sun/27.32 days per month in orbit=13.37 months per orbit.

There are those who believe that God Creates With His Words, and others who profess His Applied Language is Geometry or Calculus; but some of us have discovered that God does all of the above because He likes working out Math Word Problems.
Someone recently hinted that everybody already knows what the problems are and that one’s efforts are best directed at finding more solutions. The short answer is ‘ewes guys shore expect a lot out of 1 brain cell clinging desperately to all the missing parts of its anatomy.’ But even in this situation, the old adage holds that ‘If you give a man a fish, he eats for a day; but if you Teach a man how to fish he eats for a Lifetime (and can feed others).’

So, learning how to get a solution is more important than just providing someone with an answer, because then they can find out answers to things they think important and not just settle for solutions to things someone else feels they should know.
This is where it gets personal; during my school years, I remember having to work out Math Word Problems from as early as grammar school (thanks to Mr. Comer, Principal, PS 229; and for all those Irish Blessings that at first glance looked like curses), then deliberately throughout middle school, and by the time high school and college rolled around it seemed every math problem was initiated with a word problem.

We were not given math problems to merely hone technique or just math’s sake but the majority of the problems were tied in to real world phenomena and required having to depict or translate the narratives into mathematical relationships.
This is where those of you following this site get to LOL because you see how abysmal my math skills are right now, but that won't keep me from trying; I know I have forgotten the bulk of all that I learned—I even forgot how to integrate, but somehow I have to make this work…

And having put two children through school I am surprised at the limited exposure they each have had to applying the math they learn by solving word problems. It was only until they each reached beyond Algebra II that their textbooks or homework assignments included a slim number of word problems that they needed to work, if any, and not until Calculus did working word problems become common.
The trick is to learn how language describes math, as simple as ‘and’ means ‘+’ and ‘a collection’ means ‘a set’; higher level concepts would be like ‘marry’ means ‘unify’ and if you are working out a problem in physics it may mean ‘equalize two strands before splicing (uniting, adding, linking, merging, etc)’ ; or the word ‘soul’ may mean ‘any one' or ‘nonphysical, i.e, imaginary' entity.

Why such an emphasis on solving word problems?
For the simple reason that 'a picture is worth a thousand words'; it is simply a fast way to get a detailed concept across to a large audience in a language everyone can understand.

This is best illustrated with an example:
(وَإِنَّا لَجَمِيعٌ حَاذِرُونَ (26:56
(وَجُمِعَ الشَّمْسُ وَالْقَمَرُ (75:9
Signs 26:56 and 75:9 are written in Arabic, a language that only about 4% of the present day world population can understand.

The first translation in English (a language spoken by about twice as many as those who can understand Arabic) works out to:
26:56 And, truly, We are Wholly Vigilant

75:9 And the gathering of the Sun and the Moon
And the interpretation of these same Signs in arithmetic syntax works out to:

26:56 And, True, We are Discretely Computing/Adding Up/Gathering
75:9 And combining/calculating the 'Center of the Orbit' and the 'Time in Months'

The words discrete and calculating and adding up do indicate some type of integration is taking place.
The Sun is a metonym for the point around which other bodies revolve or the 'center of an orbit' (aka focus); and the Moon is the only natural Earth satellite and is closely linked to timekeeping.

In fact, the words moon and month are cognates and a month was used by early civilisations to mark out the natural time period of the Moon (in fact, some languages use the same word for both Moon and month, like in Farci 'mah').
Based on the foregoing, it's not a major leap to think that Sign 75:9, in addition to its prima facie message, is also a math problem. If one were to follow the arithmetic syntax and use a handy-dandy computer program to do the integration, such as the ubiquitous but quasi-reliable Excel tool, it becomes evident the problem is basically calling to attention the geometry of the orbit of the Moon around the Sun and what happens if one were to integrate or sum up the discrete values (given by the Sign numbers 75:9) from 75 to 9.
What is not clear is whether these upper and lower bounds are to be taken in Degrees or Radians (), or simply Time.
To keep the math manageable, an approximate circular orbit is assumed but that shouldn't keep anyone with more time and better tools from working out the case for an ellipse. The radial plot and the edge view (line chart) along with the calculations appear below.

Both the Radians v R and the T v (cos ^2 + sin ^2) plots are generated based on the assumption that the Moon's orbit is given by (400 cos t+ cos 13t, 400sin t + sin 13t) with the Sun at the geometric center (the focus).


The line graph depicts a close-up of the edge view and shows that the curve undulates (has 'rounded corners') without any negative curvature...


...and I hear someone say, "So, what?!" and another call "Dibs!" and Old Faithful say, 'F#*$ me!'...


The Radar plot T v R^2 indicates that a sector about 1/3 of the whole is missing. Interestingly, there is a beltway that partially circles Lexington, Kentucky evocative of this undulating orbit (generalized ellipse unwrapped from a conic surface for more than one period with interval length 2pi/k) with a similar size bite taken out of it:


________________


Depeche Mode
Policy Of Truth song lyrics
Songwriters: Gore, Martine …

It's too late to change events
It's time to face the consequence
For delivering the proof
In the policy of Truth
Never again
Is what you swore
The time before…

You'll see your problems multiplied
If you continually decide
To faithfully pursue
The policy of Truth
Never again
Is what you swore
The time before …

Surely there must be saner ways to go fishing (get it--de peche mode?)!

I guess somebody out there doesn't like working out Math Word Problems or feels threatened by something as simple as my commuting home, and that's why I have included the image below that has nothing to do with what I am on about here. And it also occurred to me (with a great deal of sadness) that nobody gets what this is really all about since I am having to deal with this type of tomfoolery still.


Just because I am slow to anger, does not mean that I don't get angry; and just because I prefer to walk away does not mean that I am chicken. But I know now why I don't see them coming, I guess it would give me a rather sizable unfair advantage. But then, that's what Mikey is for and I take back what I said earlier about your artwork Michael, please feel free to submit it prolifically; and I don't need to hear any more about my bunker mentality since after this morning's commute it appears to be well founded (the angle of incidence was absolutely perpendicular to the direction of travel (vehicle speed about 70 mph)--did You see who did it?--And, it's no use trying to break the news to me slowly and gently when the kids blurt it out at the breakfast table).

Building A Mystery

"Those in the know, Know;
...to everybody else it's just a stack of hay!"--My Mother

I know, I know, getting through A Page In The Life must seem like one must have their 'vorpal sword' ever at the ready, but there is more to language and meaning and interpretation here than synonyms, antonyms, and homonyms. A vorpal sword is a weapon used to slay the Jabberwocky and it surprised me that it recently made the Times Crossword puzzle a couple of days ago which brought to my attention another poem from Alice In Wonderland that was a spoof of the poem Speak Gently by American poet David Bates, the last two stanzas follow:

Speak gently! -- He who gave his life
To bend man's stubborn will,
When elements were in fierce strife,
Said to them, 'Peace, be still.'

' Speak gently! -- 't is a little thing
Dropped in the heart's deep well;
The good, the joy, which it may bring,
Eternity shall tell.

In some parts of the world, and I still think there are some parts of the world, the word 'Um', which can sound like 'Im' depending on one's accent, means 'Mother'. And if something has the attribute of being the 'mother of a thing' it means that it is the quintessence of the thing. Keeping this in mind the word 'im.possible' takes on a whole new meaning, and something that conveys no possibility whatsoever comes to mean 'the mother of all that is possible'---endless possibilities.
During the opening scene of The Bee Movie, Jerry Sienfeld's voiceover shares with the viewing audience that science says it is impossible for a bumblebee to fly based on the laws of aerodynamics, but the bee doesn't know that and it flies anyway. According to Wikipedia, this common misconception that bees "violate aerodynamic theory" traces its roots back to a 1934 French book Le Vol de Insectes by M. Magnan wherein he concluded that according to his application of equations for air resistance to the flight of the bumblebee, their flight could not be explained by fixed-wing calculations and that "One shouldn't be surprised that the results of the calculations don't square with reality".

But in fact this merely confirmed that bees do not engage in fixed-wing flight, and that their flight is explained by other mechanics, such as vortices and non-linear effects caused by the rotational rapid beating of bees' (and other insects' ) wings that are a vital source of lift. The vortices allow the bees to borrow energy from the swirls/vortices that form around their wings during flight.

It turns out that bees rotate their wings before starting the return stroke, and the wings are lifted by the eddies of air created on the downstroke and this high frequency oscillation of their wings means that many hundreds of vortices are shed every second to form symmetric vortex street patterns. Vortices inherently create drag and bees can recapture some of this energy and use it to improve speed and maneuverability.

Aerodynamics is simply a specialized study of general fluid dynamics, and on earth the most common fluids under flow are water and wind. Hydrodynamics explains water's action and the Aeolian processes describes wind's activity; more specifically, the winds' ability to shape the surface of the Earth and other planets. The wind erodes, transports, and deposits materials most effectively in arid environments such as deserts and in areas with sparse vegetation and a large supply of unconsolidated sediments. While water is a much more powerful eroding force than wind these types of aeolian landscapes are greatly influenced by the aeolian process and are ever changing and shifting with the wind; unless one can get the wind to 'be still'.

Wind blowing across the desert makes for shifting sand while wind blowing across a string makes music. The Aeolian harp is driven by the von Karman vortex street effect since the motion of the wind across a string causes periodic vortices downstream that cause the string to vibrate. The sounds from the Aeolian harp are random depending on how the wind blows.

In music theory, the Aeolian mode is the sixth mode of the major scale and has the formula 1, 2, ♭3, 4, 5, ♭6, ♭7; basically, five whole steps and two half steps. Led Zeppelin's Achilles Last Stand is arguably one of the finest contemporary examples of this classical music mode.

But our purpose here is not to harp on about aerodynamics, vortex streets, or aelonian music modes; eeeventually, as you may have come to expect, it all ties into what is really on my mind, and that is while many things may at first appear to be random there is no escaping that the apparent randomness may in fact be a ruse to disguise some very careful planning by an as yet Nameless One (let's call Him 'God'). {And Dear God, I know the fact that I am writing this means that I was forced into having to make a decision that Solomon himself could not adjudicate, but what the hay-- I will just keep on this track until I hear otherwise...}

قَالَ رَبِّ اغْفِرْ لِي وَهَبْ لِي مُلْكًا لَّا يَنبَغِي لِأَحَدٍ مِّنْ بَعْدِي إِنَّكَ أَنتَ الْوَهَّابُ 38:35
فَسَخَّرْنَا لَهُ الرِّيحَ تَجْرِي بِأَمْرِهِ رُخَاء حَيْثُ أَصَابَ 38:36

38:35 (Solomon) prayed: "My Lord, forgive me and grant me a Kingdom (Dominion) that will suit none other after me; for You are the Grantor of Bounties.
38:36 Consequently, We Subjected the Wind to flow gently at his (Solomon's) behest wherever he willed.

Controlling the Wind turns out to be quite a powerful force since with the proper guidance it can literally change the landscape; and the Quran depicts as much. Choosing to open with Chapters 25 and 42 and then follow with Chapters 47, 51, 56, 60 and 69 all in a row and then applying the method developed in an earlier post, A String, A Ring, A Modulos Thing, but proceeding by tens (decans) rather than singly, a similar table was established as the one for clock math in A String, A Ring, A Modulos Thing.

Surface charts and Line charts were drawn using Excel by choosing the parameters SModC, CModS, SModC/C and CModS/C in chapter order based on the decans in each chapter; 10, 20, 30..etc, depending on how many verses were in each of the selected chapters.

The data points used are the same for each chart, but the rotations for the first and third charts are x= 35 deg; y= 15 deg, z=0, perspective =5 deg; and for the second and fourth charts the rotations are x=140 deg; y= 15 deg, z=0 and perspective =15 deg.

Interpretation varies depending on the rendering, but the two surface charts resemble encampments and American Southwest landscapes (similar to the ones depicted in Eyvind Earle's lithographs) and the two line charts are remeniscent of buildings and pyramids, respectively.

And to make a long story short, this method was pursued for the first 20 chapters and the data was taken in sets of 19 until Something went Flying Off The Page.




---among others.
The Cummulative Summary charts for that particular excercise appear below as a line chart (music to my ears), Radar chart (see low order projective plane, affine transform) with the x-y axes switched (where have I seen that before?), and a Radar plot which looks like a dipiction of the 'All Seeing' Magic Eye (Iris).

_____________




The results segregated in groups of 19 without rotation:












===========Alright, Who's The Wise Guy? ...

Recall that 1 Radian is approximately 57.29 degrees.

Vive La Différence

It's funny when oui Americans try to speak French...mais non.

Before I go again, I think my Dad pbuh wants to weigh in on something:

"I have three daughters, there is my eldest, the very pretty smart one (John
met her); and the younger one, the reallly good speller (he heard of her, but doesn't want to meet her); and then there is my youngest one (meeting her was no picnic in the park...more like a day at the beach). After we had her we could only have sons. Of all the people in all the worlds she is the last one to be crazy. For the simple reason that she does crazy consummately well.

(She is a nondrinker, nonsmoker, non-recreational drug user, whose idea of a
soul vacation is to get out of school fast, become gainfully employed
in her own field, and marry for love (not money) and give birth to two children
while helping to keep her husband's fledgling business going all before she
turns 30--yes, she has a flaw--she can't cook.) 

Here is my impression of her crazy act: She is hale as a prize horse and rarely ever gets sick until one day she goes into a doctors' office complaining of an obscene amount of pain everywhere in her body and brings along a can of stuff she thinks caused it since she is some crazy kind of a chemical engineer who picked up her degree from some first rate school in New York City on a full scholarship (proud dad, can you tell?) and deduced she is suffering effects from having had a toxic exposure, only to have the doctor tell her she is crazy for coming in to his practice over the course of the past several months complaining of and being diagnosed with a host of various other ailments including but not limited to: 

asthma, tacchicardia, allergies to everything including histamine and anti-histamine, aggravated sinusitis, irregular monthly cycles, joint problems, swelling, migraines, hypersensitivity to light and sound and climate and other
neuropathy, mammary and lymphatic cysts, sleep disturbances, nausea, DTs,
skin tags that behave strangely by practically growing 2 cm during a shower and then falling off 24 hours later, and a host of other dermal, respiratory,
digestive, neuropathic, psychomotor, neuropsychic, non-viral non-bacterial kidney infections, and other systemic aggravated sinusitis, irregular monthly cycles, joint problems, swelling, migraines, hypersensitivity to light and sound and climate and other neuropathy, mammary and lymphatic cysts, sleep disturbances, nausea, DTs, skin tags that behave strangely by practically growing 2 cm during a shower and then falling off 24 hours later, and a host of other dermal, respiratory, digestive, neuropathic, psychomotor, neuropsychiatric, non-viral non-bacterial kidney infections, and other systemic maladies...but then there was also blue tinged nail beds, tears that burn her skin, out-of-body experiences, strange auditory effects that her toddler also reacts to, and yes, hallucinations that she knows are hallucinations because they are after all accompanied by screaming cluster headaches and otherwise known as aura

 ...never mind that her lab tests are abnormal, there is blood in her sputum and any medicine she is given makes it all worse! and her hallucinations get so vivid that they dress really natty and pull up in their SUV's in the middle of a busy intersection not only hearing but following directions coming from her auditory hallucinations and her kindergartner sees them and wonders aloud 'why do they look funny?' and the doctor tells her she is crazy and crying out for attention and deftly gives her a referral to see a psychiatrist.

And when it becomes clear to her the doctors do not or cannot help she makes an appointment to view her medical records because they made her doubt her own mind and she thinks she needs a reality check; and when she shows up as appointed some wild dog of an HMO administrator goes off on her and doesn't keep her wild dog thoughts to herself when she tells my daughter to take the elevator back down to hell (where presumably she came from) and calls the cops and tries to place her under false arrest for cussing and threatening her staff; but when the cops show up they see my daughter doesn't have enough breath in her body to even speak; so the officers threaten to have the wild dog of an HMO administrator arrested for attempting to make a false arrest if she does not comply with the law and give her a date and time to allow her access to her medical records; and one officer offers to walk her in on that day if she thinks they are going to give her any more trouble (she wrote him a letter to thank him)

On her return visit, she notices some key visit(s) are missing from her chart and nowhere to be found (not then, and here it is about 15 years later, and so far not ever; something did surface about 10 years later but it was more like creative writing and not what she knew took place during 'that very strange visit').

Things deteriorated quickly from there since being crazy pretty much kills a marriage where she comes from (not hell) and the only reason her husband and she stay together is because of a promise he made to me that he would take care of her and neither one of them has the heart to tell the kids (who pretty much figured that much out, but for their own reasons still prefer both parents under one roof over any other option).

And that's why We All Landed In The Psych Ward, and why everybody else on the planet gets to do crazy before she does."

...here is the subtext for those of you who keep insisting it is worth the risk; it is not that Michael doesn't eat but that he had not yet had the opportunity to wash up, since he was still in the paint during our little lunch...

I guess now you can all see why I love my Dad (and my Mom--someone please ask her to stop saying 'Land!' everytime she sees me, I find it a oui bit disorienting) so much; and why the usual manner of coming and going doesn't quite suit me...I mean, do I want to be 'born again' and have some other nice lady poop on my head? Or worse yet, be made to forget that I have my own children (surely no matter how awful my cooking it does not warrant that kind of punishment)?

That's why nothing short of a full Resurrection (Being Borne) will do; and in the matters of both coming and going, this is how we roll:

Surah 17 Al.Isra (Travelling)
وَقُل رَّبِّ أَدْخِلْنِي مُدْخَلَ صِدْقٍ وَأَخْرِجْنِي مُخْرَجَ صِدْقٍ وَاجْعَل لِّي مِن لَّدُنكَ سُلْطَانًا نَّصِيرًا 17:80

17:80 And say: "My Lord, Admit me a good/honest/truthful Entrance (Way In/Entry) and release me/allow me to depart in a good/honest/truthful departure; and grant me from Your Power an Authoritative Victory.

Surah 22 Al.Hajj (The Pilgrimage)
لَيُدْخِلَنَّهُم مُّدْخَلًا يَرْضَوْنَهُ وَإِنَّ اللَّهَ لَعَلِيمٌ حَلِيمٌ 22:59
22:59 He Will Admit them in an Entrance (Way In/Entry) that Pleases them and indeed, God is Aware (Knowing), Patient.

And that, Dear Children, brings us back around to the topic of UFOs (You Flying that (those) Object(s)?):

17 Al-Isra (Travelling)
سُبْحَانَ الَّذِي أَسْرَى بِعَبْدِهِ لَيْلاً مِّنَ الْمَسْجِدِ الْحَرَامِ إِلَى الْمَسْجِدِ الأَقْصَى الَّذِي بَارَكْنَا حَوْلَهُ لِنُرِيَهُ مِنْ آيَاتِنَا إِنَّهُ هُوَ السَّمِيعُ البَصِيرُ 17:1
17:1 Extol/Exalt the One Who Captured/Seized/Took/Captivated His Servant one night from the Holy Mosque (Ka’ba) to the Farthest (Most Remote) Mosque (Majid al’Aqsa in Jerusalem); whose precincts We Blessed; so that We Can Show/Demonstrate to him some of Our Signs that Indeed He, and Only He, Is the Hearer, Seer (All-Hearing, All-Seeing).

And why, while it may seem like I am blabbing secrets all over the globe, I publicize tightly guarded secrets with the confidence of knowing not a single word gets out except to those already in the know or the ones it is meant for:

وَإِذَا قَرَأْتَ الْقُرآنَ جَعَلْنَا بَيْنَكَ وَبَيْنَ الَّذِينَ لاَ يُؤْمِنُونَ بِالآخِرَةِ حِجَابًا مَّسْتُورًا 17:45
17:45 And if/when you Read/Recite the Quran We Create between you and those who do not believe in the Hereafter a Secure Barrier (Invisible Cloak, Secret/Hidden Veil...)

and it's all in Good Spirit...

وَيَسْأَلُونَكَ عَنِ الرُّوحِ قُلِ الرُّوحُ مِنْ أَمْرِ رَبِّي وَمَا أُوتِيتُم مِّن الْعِلْمِ إِلاَّ قَلِيلاً 17:85
17:85 And they will ask you about The Spirit, say: "The Spirit Is At God's Behest and you have not been given knowledge/information about it except a little."

___________________________________________________

"In women, courage is often mistaken for insanity."--Doctor in Iron Jawed Angels