Friday, December 31, 2010

What would have you done if you were Li Cunxin?

Li Cunxin (b. 1961) is, at first sight (first time I heard of him, today), a most surprising case of success and achievement.

It is certainly striking his becoming of a good ballet dancer, from a totally fortuitous contingency (story explored in Bruce Beresford´s movie). It seems that he could have been any kind of professional the Coummunist party or chance would have him wanted to be, from a mathematician to a chess player or a gymnast. Moreover, it is stunning to learn that years later he pushed his way through into finance and accounting and became a stockbroker. And even more shocking is to know that Li is now a Senior Manager of a large stockbroker firm in Australia (didn´t find its name in google), a best-seller author and a prestige, renamed speaker with experience over 200 presentations in "corporate meetings, seminars, events, industry conferences, associations, business leaders retreats, literary festivales, universities and schools". He was even awarded as 2009 Australian Father of the Year! (http://www.licunxin.com/).

The movie has not made a deep impression on me, nor moved sincerely, though. I suppose the dubbed-version has to do with it (when will we stop dubbing movies here?!). It is too much a tear-jerker, or intend to be. Characters are not deep nor developed enough to make the story genuinely emotional and touchy. The story runs too fast and shallow. I got the impression of being a driver precipitating himself to the end of his destinity from Madrid (Central Spain) to Murcia (South Spain), roughly 250 miles, with his head fixed on the highway, no stops, missing a vast variety of landscapes and colors and corners and peculiarities _A familiar impression from my times as a Sales Engineer.

Technically I liked the light and fotographs of the miserable villages, but certain details are poorly treated and some others are clumsily presented (for instance, a just-arrived Li into Houston, looking up to the tops of huge skyscrappers, to avoid the problem of modern cars mismatching the setting of 1981, a stale topic as well). Generally, it lacks development... Perhaps, the book is better... Does anyone have read it?

If I knew how to do a movie, I would have focused on an episode of Li´s incredible adventure. The most fascinating scenes of the story are the ones of the kidnapping in the China Consulate. Li seems to be truly in love with Liz (I would) and decide to stay in the US for her and marry her in secret, acting in collusion with Liz and two other friends who, by the way, seems to selflessly care for him and be attached to individual freedom principles. The very night the Houston upscale society gathers for Li´s farewell, they released the news to Ben Stevenson, Artistic Director of Houston Teatre and Li´s mentor, nicely portraited by Bruce Greenwood (the best in the movie, along with the lawyer).

The following part of the story is amazing: Li and the rest, all confused, worried and much aggravated showed up at the Consulate, where they are deceived and Li is retained by force. The characters refuse to leave the Consulate and the conflict scalates progressively up to Vice-presidency scale. It was something like 21-hour kidnapping.

This is the part I would have choosen for my movie!!

Now:

My First Comment: I walked home from the movie theatre considering that secondary characters in this episode are the real heros. What is indeed the purpose of them by staying in the Consulate, and by defending Li´s interests? For it is clear: Li struggles to satisfy a personal interest. But, again, why did Liz, the lawyer, the two friends and Stevensons behave in an apparently much unselfish way? Only the lady seems to have an expected reaction. Paradoxically, she plays the role of "weak, twisted woman" in the scenes, as the watcher has alreay been placed on Li´s side a long while ago.

Indeed, regardless undeniable Li´s merits, his fate is conditioned to the actions of a reduce group of individuals who seems to act generously. A second example of these people is the anti-revolutionary first professor of Li, whose desire is to see him dance at the end (art interest). Truly touchy, this character!

My Second Comment: This character I just mentioned, along with Stevensons, are indeed vocational characters. Li Cunxin is not (in spite of his official web page saying otherwise). He is determined, fearless and display an extraordinary level of achievement, but he is not vocational.

My Third Comment: In a sense, I do not see Li Cunxin as a recipient of all virtues that pundits wants to see as a whole for motivational speeches (as his official page also points out). He is, of course, a carrier of some of them (again, courage, determination, sacrifice aiming to pursue his personal goals). The problem is that I see, in his particular case, some others (love, gratitude, obedience, faithfulness) in contradiction with the previous ones which, obviously, Li does not fulfill.

Take, for instance, the following statement from the Welcome page of his web: "(...) Li recounts his determination, perseverance, vision, courage and hard work, and in particular, the sacred family values and integrity that he learned in poverty-stricken China, which has driven him to become one of the best dancers in the world". This statement is topic-stinking and absurd according to the movie I watched today. Just remember: the first nights in Peking, Li child moans, and he recovers his smile after another boy farts intently!! If I must be more spiteful... How can family values be sacred for Li if he chooses and prefers his career upon his family and remains with no news from home for years!!

My Fourth Comment: Li´s fate is entirely made out of the actions of individuals. Even the govermental employees who picked Li up did it just because a rural teacher said: "Did you care to consider again that boy over there?".

Any system denying individuals their right to choose their paths is barren. Life and Society are made of individuals.

My Final Comment: I am in love with Liz. She looks so good, so neat, so fresh and innocent, so sweet and tender... You know? If I were Li, my story would have ended that day when, packing our things to go to Florida, Stevensons tries to convice me to stay in Houston by plunging a contract on the table. I´ve have said to him: "I will ponder on it", and as soon as he had stepped in his car, I would have kissed Liz and told her: "Hurry up, dear, please, we are leaving now. I want to love you for the rest of my life. That´s why I came to America. Oh, God, I can be whatever I want in America".

And you? What would have you done if you were Li Cunxin?

Thursday, December 30, 2010

Fresh wine in mature wineskins

Only if our affairs are expendable, we can afford throwing them away and starting from scratch _A clean cut. That is called "a new beginning".

In the Christian tradition, however, such "a new beginning" is understood differently. We, humans, are defined as creatures of God, unique and irreplaceable. Our life and history, no matter how punished or blessed, have sense and meaning, and past and memories, flesh and mind, rights and wrongs will not  be detached since they conform us and are unrepeatable.

Therefore, when the time is come, the judgement won´t expurgate just the righteous amongst the all to keep them apart and dispose of the rest, but nothing will be spared. The "new beginning" will indeed be a "renewal" (no clean cut), as filling the mature, old wineskins with fresh wine. Our worn-out self will be restored.

As unique creatures provided with inherent value, we humans become the most prominent feature of Creation. God assigns Man the kingship over Nature; most important, Man is endowed with the sovereign of his life, purposes and choices, is invested with freedom, and becomes the sole master of Himself.

The importance attached to humans is of unparallel dimension, to the extend that God, the One, Lord of History and Nature, became one human, and was equal to us except in evil. Particularly, He embraced love and pain (suffering, sorrow, confusion), two hinges of human mystery. Even more, as to underline the indissolubility of Man and his freedom, Christian God did not steal or borrow a child of flesh to incardinate, nor bribed or forced none, but asked for permission, as a fine, polite young boy, and wait for a woman consent: Fiat!

So Man is of the utmost importance. None and nothing will be spared. Precisely, the rejected shall be the key stone in the building of the kingdom of redemption (Sal 117, Mt 21, 42).

Bring the mature wineskins from the lumber room, boy! We will pour the fresh wine in them, they will look so neat.

Tuesday, December 28, 2010

It is not annoying anymore, but just silly

As far as I know, the concept of assertiveness in the form it is known today was developed by a reduced group of American psycologists in the 70s. Among them, I recall that therapy was mainly divulged to the public and laymen by Manuel J. Smith, from UCLA, with his When I say no, I fell guilty. The book was a tremendous success, a real must, and twenty years downstream, at least here in Spain, theory and therapy were well-established in Psycology curricula as well as in courses of continuous-education for employees, from first-sector industries down to business and finances.

I can say that, in spite of lots of deviations and misconstructions occur over decades of practical applications of assertiveness principles by therapists and scholars (as it might sound natural), I find the technique derived from its fundamental points quite a neat and an elegant one, very useful to achieve high levels of quality in one-to-one communication, as much as in conflict resolutions (the number of cases to be applied are countless). Though I am aware of new improvements and corrections done to the main original core since then, I ignore the to-date implications, ramifications and current directions of research and clinical practice.

Anyhow, I am fond of the concept of assertiveness developed by Smith in his book and I find it once and again applicable and useful in my daily life.

The basic grounds of assertiveness are, in my understanding, as follows: 1) Out of the interaction with our fellowmen, conflicts arise; 2) We are not very different from animals in the responses, except that our brain has evolved and added some extra layers to our reptilian original nervous system; 3) As a consecuence, we humans have the option to respond to external estimuli in a new way, different from the two basic animal responses: aggresive and pasive ones; 4) The new way, assertion, allows us to construct communication schemes of better quality, reach agreements and develop high-levels of mutual respect.

The backbone of assertiveness, around which revolves the therapy, is repeted a thousand times by Smith as follows: Individual A may wish to have B do something, something A needs or, simply, something A wants B to do. The same is valid for A wanting B to behave in a particular manner or to think such and such or to work at this and that company, etc. If A does not behave by means of assertion, it might tend to use more primitive techniques, provided he holds some advantage respect to B and knows how to use it. One of those techniques, clearly aggresive, is manipulation. The impact of the theory is even more dramatic as, in a score of cases, individuals A and B are attached by strong emotional ties (family, friendship, partners, etc.).

You may notice how usual and how difficult these situations are, precisely because of the emotional strings between A and B. The typical example consists on not lending my car to my brother-in-law as he askes for, because I don´t want to and that would make me feel bad and, at the same time, remaining unaltered against any possible manipulative statements ("I don´t undestand you", "Are you ok?", "Don´t you trust me?", "Remember what I did for you when...", "It will only be a moment", "You know how much careful I am", and so).

Manipulation can be exerted in 3 common directions, according to Smith, etc.: to get you feel anxious, ignorant or guilty. You can easily pick up examples of each of these manipulations.

Many manipulative actions of the sort can be found in parental control, any time a dad or a mum, probably with best intentions, but mistakenly, try to have their kids do what they want. The amazing thing is to find the same actions in public institutions against the citizen!

Particularly to me, traffic police in Spain has always been a little too much paternal and abusive against the common driver, but it gets worse still! Neon signs like "Thanks for not speeding" or "Remember: it is better to be late than never"; Radio-station adds such as "He has no legs now" or "You can keep someone waiting on you for ever" are as much annoying as manipulative in the sense discussed before.

Today, as I drove to Madrid, I spot a couple of times a neon sign on the road: "Parking lots full downtown: this Christmas, use public transportation". It was obviously a lie (I did park my car), the same sort of falacy a parent will build (mistakenly, again) to lure his kid.

It is not annoying anymore, but just silly.

Monday, December 27, 2010

If I can dream

Wouldn´t be happy with no Religion; wouldn´t be happy with nothing to die and kill for; wouldn´t be happy with no parting love from my country fellowman; wouldn´t be happy with no country; wouldn´t be happy with no properties, no intimacies, no secrets; wouldn´t be happy being stripped of my individuality; wouldn´t be happy with peace primordial to freedom, wouldn´t be happy, I certainly not, without hope.

The later is just all the crap Mr. Lennon yearned for, well... imagined.

As opposed take, please, this beauty below. The voice is Elvis´,  a great Southerner, Gospel bred... O, God! Thanks to Freedom and Internet we can remedy lagoons of idiocy.

All Man should have them!

***

If I can dream

http://www.goear.com/listen/699330a/if-i-can-dream-elvis-presley

There must be lights burning brighter somewhere
Got to be birds flying higher in a sky more blue
If I can dream of a better land
Where all my brothers walk hand in hand
Tell me why, o why, o why can´t my dream come true
O, why.

There must be peace and understanding sometime
Strong winds of promise that will blow away
All the doubt and fear
If I can dream of a warmer sun
Where hope keeps shining on everyone
Tell me why, o why, o why won´t that sun appear.

Were lost in a cloud
With too much rain
Were trapped in a world
That´s troubled with pain
But as long as a man
Has the strength to dream
He can redeem his soul and fly.

Deep in my heart there´s a trembling question
Still I am sure that the answer gonna come somehow
Out there in the dark, there´s a beckoning candle, yeah,
And while I can think, while I can talk,
While I can stand, while I can walk,
While I can dream, please let my dream
Come true, o, right now,
Let it come true right now,
O, yeah.

Sunday, December 26, 2010

Complex representation for armonic waves

No less than sixteen years ago, I was assaulted by a question, posted in my high-school, junior-year phylosophy book: "Show that exp(i*2Pi) = 1 and explain its importance".

It is shocking to notice how many years have been gone having the question unanswered until today: as part of my new studies, I have it understood. What was I thinking to not be able to figure out before? Why could this happen? The fact is not isolated, I am afraid.

There is a couple of very common phenomena in Nature, much shunned and seriously forgotten in Schools and Academia, to which a score of real problemas belong to: diffusion and wave phenomena. Particularly, the wave motion is indeed a perturbation which, no matter its form, can be described as a superposition of sinusoidal, harmonic equations, and that´s the convenience of studying harmonics. In addition, as the mathematics of such waves is rather complicated and inaccesible as we pose realistic and accurate problems, the alternative representation by means of complex exponentials just come so precisely handy and resolutive.

And that´s the advantage of writing a sinusoidal motion as an exponential and its importance. The formula exp(i*2Pi) = 1 indicates a very intuitive and real fact of a harmonic wave: its periodicity. This is because the function exp(z), where z is a complex number is:
exp(z + i*2Pi) = exp(z) * exp(i*2Pi) = exp(z) * 1 = exp(z)                   (1)

Thus, the exponential representation of wave motion gets along well with reality.

Now, why exp(i*2Pi) = 1?

The answer has been a mysterious for a mind like mine, so much untenacious for a number of years. For an extended period of time, the Eulerian relation
exp(iθ) = cosθ + i sinθ                                                                         (2),
was largely retained by heart.
Now, it is all clear. Let´s start from a representation of a complex as
z = x + iy = r (cosθ + i sinθ)                                                                 (3),
where r is the norm of z vector and θ is the director cos(-1) respect to the real axes (angle with that axes).
Let´s take an unitarian complex number z´, for which r = 1. Thus:
z´= cosθ + i sinθ                                                                                   (4)
A differential of z´ is:
dz´= - sinθdθ + i cosθdθ                                                                       (5)
By multiplying in both sides of the equation by i and rearranging:
idz´ = - z´dθ                                                                                             (6)
Now, we separate variables and performe the integration. It results:
ln z´= iθ + C, being C the integration constant.                                       (7)
According to our representation of the complex number, based on Argand´s diagram, C must be 0, as for θ = 0, z´= 1. Thus:
z´= cosθ + i sinθ = exp (iθ)                                                                    (8)
The mystery is solved in 2 minutes!
The equation from which I started this discussion is readily seemed from (8), as z´= 1 when θ = 2Pi.
Furthermore, it is very convenient to treat formally the math of wave motion as complex exponential and at the end of derivations or when eventually the result is available, just take the real part of the complex final form, as that will yield the real solution for the problem.
Further verification:
For instance, prove that ψ(x,t) = Re[A*exp(i(ωt - kx + ε))] (1-D harmonic equation of motion) is equivalent to ψ(x,t) = A cos (ωt - kx + ε), which might clarify why the cosine form is preferred in textbooks to that of sine.
Solution:
From the basic math, the real part of a complex number, z, is calculated as:
Re(z) = 0.5 (z + z*)                                                                              (9),
where z* is the conjugate of z. In this case, then:
z = A [cos(ωt - kx + ε) + isin(ωt - kx + ε)]                                           (10)
Thus:
Re (z) = A/2 * [cos(ωt - kx + ε) + isin(ωt - kx + ε) + cos(ωt - kx + ε) - isin(ωt - kx + ε)]
                                                                                                             (11)
And, then:
Re (z) = Re[A*exp(i(ωt - kx + ε))] = A cos(ωt - kx + ε)                      (12)
q.e.d.



Foundation Statement

To whom it might concern:

1. This blog is an exercise of continuous writing in English, language which is not my first. I determined my self to publish and show one new column every day but, much intently, no less, and no more. Though I may dislike some of the postings in a later moment, whole or partially, or just regret an unfortunate sentence, considered unnecessary on a second thought, I discipline my self to not modifying anything once the "Publish Post" button has been pressed. Presently, I only made a change so far, which is to use "Growing Pains" as the title for the post originally published under "Fatherly Advice".

2. As head of this blog the three first verses of Dante´s Inferno shall appear. I acknowledge now that I have not read Dante´s Divina Commedia so far, but those verses made a lively impression on me, first time I took notice of them. At that moment, I found myself as lost as the poet in a tupid, dark, rain forest, lured by evil, and having "the beast in me caged in fragile bars" strugling to break free. The verses just fit to tight to my impressions. I am about the same age Dante was when wrote the Inferno, and -as I have wondered how I will die-, believe that am close about the middle of my life, as well. From here, the title for this blog came readily. Too tremendous? Well, these are my frightens.

3. You shall not find in this blog any contents of pornography or explicit sex, nor any ilegality, nor any call for uncivil actions. Every other time you will find bad language, because its use will seem to be a better option to convey a message or, paradoxically, is even more aesthetical.

4. I am fascinated with the dark sides of human beings, those creatures who, despite their resilency and stunning capacities, can be as fragile and frailty as fine glass.

5. I declare here a strong commitment with sincerity. I am a truth and trustful guy, you have my word for it. All pieces of information, documents, assertions, stories and anecdotes are veridic to the best of my knowledge, and do not pursue any conceal purpose or to deceive. Although,  I take exaggerations and, sometimes, boutades a most useful polisher and literary tool for situations where facts are not primordial.

6. "The foremost of all the forces that drive the world is falsehood", stated J. F. Revel. Lie and falacy is a necessary overcoat of wide collars to protect our inners from the external menaces, a sort of tight gabardine suited for our psycologies. I state now my commitment with truth and the disposal of such accesories. Most of all, I shall appear naked if needed, though I will feel uncomfortable.

7. You might find some or many of my ideas and thoughts unfocused, biased, deviated, even distorted, erroneous or ridiculous, perhaps some of them stupid or nonsensical, that´s ok. Complementary to statement 5, I want to claim here my right of being wrong as part of my undeniable freedom of expression.

8. This blog and its contents, letter by letter are my property, and I am the responsible for it, but only for it.

This is my game, these are my rules.

Alberto H. Barral
December 2010

Saturday, December 25, 2010

Gay

Christmas Eve´s dinner.... What shall I write when I am drunk?
Too many folks in love with you, that is overwhelming.

In 1985 I was 6 or 7 years old. My parents used to spend days, mainly Saturdays, in the country: friends, brothers, cosins and us, little children. Tino & Miguel were a gay couple. Homosexual and gay. Have wonderful memories of them!

Recently, years ago let say, they split. However, my sister tells my mother´s story: she was about to drop the kids (sister and I) at Tino´s place, on Saturday, and Tino phoned: please, do not bring the kids, I can hardly move here in  bed... (!!!) Mavellous story from 25 years ago, do not think you?

FUCK YOU. We already have gay people that many years ago and they love us, wiht no body to tell us what to do! No more left of that, I am afraid, today just a fucking mode.

A fucking disgusting message for Christmas, hmmm?

Friday, December 24, 2010

An ordinary man

In our desperate seek of fotune, we are inexorably animated by a centrifugal force or outbound stress that lead us away: new experiences, new people, new places. A nebulose of thatches of light diverge then our vision in an array of luminosity as much rich as vague. But even the most adventurous idles return to their origines at some point in life or even with a certain periodicity and, at once, all thin, needle-like threads of light converge into a clear vision. The come-back home operates a similar effect as that of an Iceland Crystal when moved into the right spot against a light _A clear and distinc stream, though an unique one in the case.

With all the visual angles converging, the outsider grasps an unique sensation of himself, and even the new events from abroad stand anew and fresh. So it is such a strong centripetal push that yield to a truthful sense of ourselves.

I always have this kind of feeling when I come back. My would-be brother-in-law just recalled to Juan Ramón Jiménez´s walk to see his town after he came back from the States. Very so indeed, the best perspective of the world is the one you fancy from home as it is the prayer that comes in secret after the battle amidst the crowds. Noli foras ire... .

The merging of diffracted vision into a well-defined thread of light upon my come back today, the melting of complexities in fundamental emotions and memories made me feel as one more in the lot, just a ordinary man going through life. Above all names and pretensions, hopes and presumptions, credulities and falacies, wants and impatiences, goals and deceptions, failures and successes, I am no more that a young, ordinary man, whose only touch of uniqueness -a blessing indeed- is being loved by a mother.

Salamanca, España

Thursday, December 23, 2010

Uneasiness

At this hour of the night, having finished my packing and done the major prescriptive shopping of the outsider who lives in London, I feel somewhat uneasy about my flight or no-flight tomorrow morning. It is a sort of mild anxiety I have been sensing for the last 2-3 days.

I hate lines and places overcrowded and jams and people sprawls, all that make me sour, and can do it actually tomorrow, as the probabilities of a major inconvenience are high.

Perhaps, I should take these things not serious at all.

I could not say for past Christmas, but this year I really look forward to coming back home and be around my parents (especially) and my sister and rest of the family and friends for a few days. Good company, true wishes with good wine, good food and relax. I guess this is what we meant by home, when we say home.

Ok, I am going to bed. This issue with the plain disruption in London airports have made me reflect again about solidarity, a term absolutely manipulated, abused and prostituted. To dig deeply for its original sense we all should plunge money any time we say the word as to get the foliage cleared out the way. I might try to write something these coming days and put together two or three ideas, now that it is The Season.

And there is another couple of thoughts to write down now here, but are not well-settled, am tired and, as I said, feel a little uneasy.

So
Hickory, dickory, dock,
The mouse run up the clock;
The clock struck one;
The mouse ran down;
Hickory, dickory, dock


Night, Night... My dear Beatrice.

Wednesday, December 22, 2010

Camillagate or the Tampax Scandal

Well, as my friend Esra Bulbul would say, I just learned about it.

Lady Di died in car accident in the end of August 1997, and most of what I can remember is that everybody loved her, everybody hated him. I finished in the bus the book of London by Paul Tournier -finally, a deception, shallow and superficial- and liked the epilogue, where he tells the story of Milady, Charles and Diana, and that's how I learned about.

Learned about the story of the Tampax, when everything went public. So, so, so funny!!! I could not repress a burst of laugh, a very spontaneous, enjoyable laugh. I have searched for the audio, but could not find it either. Part of the dialogue, though, I got from a published paper in Sex Roles (2006, 54, pp. 347–351) by David Linton. After a quick look, seems surprising to me that someone can seriously spend time in studying the following conversation with scientific pretensions (?!!!):


Charles: Oh God. I’ll just live inside your trousers or something.
It would be much easier!
Camilla: (Laughing) What are you going to turn into, a
pair of knickers? (both laugh) Oh, you’re going to come
back as a pair of knickers.
Charles: Or God forbid a Tampax. Just my luck! (Laughs)
Camilla: You are a complete idiot! (Laughs) Oh, what a
wonderful idea.
Charles: My luck to be chucked down the lavatory and go
on and on forever swirling round on the top, never going
down!
Camilla: (Laughing) Oh, Darling!
Charles: Until the next one comes through.
Camilla: Or perhaps you could come back as a box.
Charles: What sort of box?
Camilla: A box of Tampax, so you could just keep going.
Charles: That’s true.
Camilla: Repeating yourself . . . (Laughing) Oh, darling I
just want you now. (Graham, 2001, p. 241)


I have looked for the 1993 interview to Charles, when he confess publicly his long, long relation  with Camilla, but have not founded. Instead, of course, it is readily available in You Tube that of Diana, which I post here, for you to watch it completely.
http://www.youtube.com/watch?v=RR00zvbz9hU&playnext=1&list=PLE64AF76A8E0AF9DC&index=9

I have not done it.

Again, after a quick listening, do not like the sad countenance of Diana, do not like her way of looking, do not like her speech, but I guess it is a matter of time to start loving her, as you love a sit-com after some time, though you found it annoying when watched it for the first time.

The name itself given to the affair, Camillagate, clearly referring to the Watergate, I would say, sounds unbearable ridiculous... Seems like every affected and mousy journalist or journalist corporation needs his "****gate". Well, here it is mine-

myyyyasssssssssssgate.

Tuesday, December 21, 2010

A simple problem on vorticity

When we "agitate" consciously the coffee in a cup or the rinsing water in a glass while washing dishes in the kitchen, we observe the so-called "vortex", i.e. a depression of the level of the surface of the liquid, the largest at the middle point. We have seen it a thousand times.

As part of my review of things long time ago forgotten, I want to go through calculations and confirm that, after proper handling of Navier-Stokes equations, this phenomena is well-predicted, as the free surface of a liquid with pure rotational motion is described by the equation of a parabola.

Statement: Find the surface of constant pressure (atmospheric pressure) of a uniformly rotating bucket with constant angular velocity, Ω,  full of an ideal fluid, under gravity, g, so the velocity components relative to fixed Cartesian system of reference set in the middle point of the cylindrical base of the bucket is u = (-Ωy, Ωx, 0) (Acheson, 1989).

One might be tempted to take the apparently gentle shortcut of Bernoulli's equation: the quantity, H, applied to any two points within the fluid must be constant, C:
H = p/ρ + 1/2 u^2 + gz = C                                                  (1)

The vector u squared is
u^2 =  Ω^2 (x^2 + y^2)                                                       (2)

According to the reference taken, at the point in the surface z = z0 and x = y = 0 (i.e., middle point), p = p0 (atmospheric pressure). This condition yields the value of constant C:
C = p0/ρ + gz0                                                                     (3)

When equations (2) and (3) are casted in equation (1), we obtain the pressure at any point:
p/ρ + Ω^2 (x^2 + y^2) + gz = p0/ρ + gz0                             (4)

To obtain the equation asked (free surface), we impose the condition that all points of such geometrical place (x,y,z) must have p = p0. By doing so:
z = z0 - (Ω^2/2g)*(x^2 + y^2)                                              (5)

Unfortunately, equation (5) does not make any sense. The last term in the RHS is always positive and so it appears that the highest point of the surface is the middle point, which is radically opposed to physical observations (a "surge" in the middle point, instead of a depression).

The root of the mistake lays in considering that Bernoulli's equation is applicable to any point within the fluid, and so to any point within the surface. This assertion is only valid when the fluid is irrotational (i.e. ω = curl u = 0). However, the flow given has vorticity, ω = (0, 0, 2Ω), which is not zero. Bernoulli's equation would be only applicable to points within the same streamline, which is completely different from two arbitrary points of the profile of the free surface.

To solve the problem, we need to write and apply Navier-Stokes equation to the problem. In this specific case, they are:
x - component:     - Ω^2 * x = - (1/ρ) * (δp/δx)                   (6)
y - component:     - Ω^2 * y = - (1/ρ) * (δp/δy)                   (7)
z - component:                   0 = - (1/ρ) * (δp/δz) - g              (8)

The three partial differential equations (PDE) can be integrated individually, without forgetting the integration functions as:
x - component:   p = Ω^2 * ρ * (x^2 / 2) + f(z,y)                 (9)
y - component:   p = Ω^2 * ρ * (y^2 / 2) + f'(z,x)                (10)
z - component:   p = - ρgz + f''(x,y)                                      (11)

A particular solution is a linear combination of (9) - (11), plus a constant. In this case, it is readily verifiable that equation (12) is a solution for (6) - (8):
p = ((Ω^2 * ρ) / 2) * (x^2 + y^2) - ρgz + C                        (12)

Now, re-using the boundary condition applied before to reach (3), C = p0 + ρgz0, and so, the general equation for the pressure of any point (x, y, z) within the liquid is:
p - p0 = ((Ω^2 * ρ) / 2) * (x^2 + y^2) + ρg (z0 - z)            (13)

Every point that belongs to the free surface must satisfy that p = p0. If this condition is applied to (13), we find the solution to our problem:
z - z0 = (Ω^2 / 2g) * (x^2 + y^2)                                        (14)

Now, the mathematical equation represents the correct parabola and reflects the depression of the middle point (lowest value).

The same result can be obtained if we work directly in cylindrical coordinates, with uniform and circular velocity, and only azimuthal component, (Bird et al., edition 2007):
z - z0 = (Ω^2 / 2g) * (r^2)                                                  (15),
where, r is the inner radius of the bucket.

Exercise: Write and solve Navier-Stokes equations in cylindrical coordinates for this problem. Verify result (15).

Comments:

1) Acheson clearly states that vorticity does not mean circular motion. In this application, a pure circular (rotational) flow has vorticity, but take for instance, the simple 1-D flow between parallel planes of an ideal fluid with u = (βy, 0, 0), no rotation at all. It is straightforward to see that ω = (0, 0, -β), so the vorticity is not zero.


2) What it is normally called "vortex" appears in fluid mixing and other application where the rotational component of velocity is predominant over the other two components (radial and axial), and suggests that the mixing between adjacent layers of fluid will be poor. Intuitively, however, it seems to be just the opposite.

I can now recall my days in Vintage Pharmaceuticals, Huntsville, AL, with all those liquid-liquid mixture applications and that large number of Batch Product Records long having written instructions as: "set the impeller at such and such RPMs and wait for the vortex to be formed", and the long discussions with Y. K. about the possible partial inadequacy of it.

The thing is now remembered... And, flares and bitter fevers set aside, Y. K. mentioned it in his nice recommendation for me benefiting the admission in University College London.

Sunday, December 19, 2010

White, white Christmas

It was a good snowing in London on Saturday. Quite cold. Up here in Muswell Hill, about a quarter of an hour after I was looking through my window the frozen trees it started to snow and settled almost immediately. Vehicles were unable to make it to the top of the many steep streets and buses and all were stranded along the road before the upper point in Highgate Station.

During an hour, the predominant color was white, clean and pure white. Along with it, SILENCE came. No cars, no buses meant silence, and the sound of flakes falling on the umbrella or somewhere else is as attenuated as a pin dropping on a carpeted floor. And no birds, no natural life, apparently. A white death.

Significantly, to the general degree of quietness by-standers in general contributed. Apart from children shouting, folks remained in silence. Better to say, all looked as dumbfounded by the vision. It is a stupid interpretation, I know that, but it seemed to me as we folks distrusted such quietness with great respect, fearing perhaps that some undefined creatures were lurking to get to us and bring that cold and silence to our within as well.

Oh! How sharp and burning the combination of cold and white silence can be... .



A nice discovery has been The Screen on the Green movie theater in Angel Islington. It showed today the 1946 Capra's "It is a Wonderful Life", a true Christmas story for adults. It has been a surprise as well, for the 200 seats (I calculated) were sold-out (in fact, mine was the last ticket!). And mostly young people. It is a tale from a time where movies told stories, a long 2 hours to laugh and enjoy while you drink a cup of coffee or hot chocolate or beer, and let some tears be upon your face (I have come to the point where I need to cry once in a while and I need to watch movies to be able_ Is that good or bad?)

I had to go to the restrooms in the middle (must have been the cold + the beer) and my feet were not warm enough, but still, a nice, nice time... Even being on my own.

If I have to pick 2 favorite moments I would choose: Second, at the end, George Bailey running to meet his family, stumbling, tripping over the snow once and again and yelling like crazy: "Merry Christmas, Merry Christmas!" And first, at the beginning, the Mary girl bending over the counter when George boy is serving her an ice-cream and whispered in his deafened ear: "George Bailey, I love you since the first day I set my eyes on you...".

The movie has 200 hundred moments like these... .

Fatherly Advice: Remarks on good education

Being said that looking for a reasonable explanation to everything is not reasonable, particularly when coping with the difficult task of evaluating fatherly performance in the education of our kids, it must be said that naturally not everything is out of control. Even more _Most of times, someone is to be found accountable and responsible for a kid breeding and the particular output of it.

Of course, let's not consider the cases of clear disorders, such as hyperactivity, depression, autisms or attention deficiencies, etc. Not even the disorders origined from the kid inability to occupy a healthy niche amongst his pairs, more or less hostile. The difficulties are many.

However, lets now underline the importance of conveying a good education to the offspring.

Generally, in most cases, any time a kid grows up and develop a conflictive conduct when a teenager or youngster, such a conduct can be described as anti-social, in a most strict sense: that inability to run their lives along with those of others. I find this inadequacy beyond any code of moral convention. There is a clear distinction between being unique in terms of a life proposal and being anti-social. The unique, rare or nerd is content and his ties to society are strong, regardless his carelessly attachment to accepted social manners and modes, as he lives along with and amongst others.

However, conflictive (and, in many cases) delictive attitudes, cast the perpetrator outside the social circles and his reflection of himself signifies clear discontent and the sense of belonging somewhere else, an else that might even not exist.



So here it is my point: the struggle of parents to covey a good education to their kids is a battle to put them in the social game, to deeply sow in them the roots of the sense of membership. In modern societies, that membership, as said, can exist regardless strong individual lifestyles. Those roots will be channels for future happiness and health.

Good education means interaction, social zeal, the realization that the gravity center of this so-called life is not within ourselves, that we have no granted rights, that the mystery of life is a stronger than us and will remain here much more after us, as it has been here since much more time before. That we are nothing more than anyone else.

I am having breakfast in a overwhelming snowing morning and there is this couple with a 4 or 5 year-old child, named Harry, and the boy is a nuisance. And all his parents do is contemplate him with milds "Harry, do not do that, Harry, do not cry, Harry, Harry", but naturally they do not mean it, and Harry is having confirmation every 1 minute that he is doing something not allowed, but for him, he is allowed, so he is more.

You are in a plain and next to you there is a boy, and the child is a nuisance and has a tremendous high-pitch voice, perforating your ears, and his mother is only: "Schssssss", every other ten seconds. Again, she does not mean that. So the boy is reassured that he is something more.

One wishes quite often to be considerate by others as one tries to be. To me that is all education can be accounted for. I feel it has been so since the very beginning and, as the stronger and more genuine institutions, such as Family, this fact is not stated originally by any theory of political or social organization _It is just written in the brains of the Homo sapiens to escape, day by day, the primitive wilderness.

Recomposition can start from a very simple and truthful: "Thank you".

Saturday, December 18, 2010

Husband or lover

Saturday morning. Laziness and irresolution. From my chair, and looking up through the top-side window, the beauty of the cold, ice-water droplets clang to it and the naked tops of black trees, with their thin, upper branches piercing the undefined mass of grayish sky, straightly frozen into it, lead me astray, as one wishes to capture time and get it rather here, motionless, as like in a photograph, but to use and enjoy it in so many different ways at the same time, with no remorse. And so my life flows, determine-less, with parts of me pulling and straining in opposite directions, as many as you can think of.

Sontag gives some qualities of a husband: reliability, intelligibility, generosity, decency, moral goodness. And also she gives out qualities of a lover: temperament, moodiness, selfishness, unreliability, brutality. "And, as in life, so in art both are necessary, husbands and lovers. It is a great pity when one is forced to choose between them" (Camus' Notebooks, 1963). Is that us men tend to choose between as well?

The problem might not be the election, but the level of attachment we are able to maintain to such choice. Perhaps, women really look for one thing or the other and some women actually need both husbands and lovers, but all are reluctant to accept hybrids.

And here upon lies the tragedy of some men, whom have been shaped neither in one form nor the other by inner, unattainable forces. There you have, I can think of, some young beggars, faithful as dogs, tender as summer nights (the comparison is inevitable), who have lost their decency and self-pride, but would be reliable if only someone they care of could touch their hearts before the no-return state. There you have, on the other side, so attractive big motherfuckers, brutally dishonest and frivolous, but just too selfish to cast their lives in a vulnerable state.

"Again, as in life, so in art: the lover usually has to take a second place. In the great periods of literature, husbands have been more numerous than lovers; in all the great periods of literature, that is, except in our own. Perversity is the muse of modern literature. Today the house of fiction is full of bad lovers, gleeful rapists, castrated sons _but very few husbands" (id.), and that just puts some of us out of the equation.

Growing pains

Michel Lohan & Billy Ray Cyrus, daughter-suffering-from fathers in distraught.

It is nowadays clear we want to KNOW. We need to search for the meaning of things, provided everything has it, and  adjust ourselves to a mechanistic way of live: whatever happens, either good or bad, must have a causal-effect model that explains it. Our moral schemes and securities must prevail, around which the whole world gravitates.

However, it is just too painful to recognize it is not like that at all.

"The function of criticism should be to show how it is what it is, even that it is what it is, rather than to show what it means. (...) Equally valuable would be acts of criticism which would supply a really accurate, sharp, loving description of the appearance (of a work of art)" (Susan Sontag, Against Interpretation, 1964).

The claim of Sontag in the 60s against interpretation holds his entirely value today in a broader sense, and can be extrapolated: "The mystery of the world is the visible, not the invisible" (O.Wilde). Let's try not to understand, but live. And so the mystery of naughty children who are lured by evil is just that _A mystery, a Mystery. There is not a plausible explanation for it, nor anyone can be taken responsible for it.

I would like to record here 3 fatherly advices that are to me master pieces of respect to the mystery of life. At the same time, accounts for a great educational value. Its virtue consists of accepting life as it is and ask for abidance to future generations.

1) Atticus Finch, To Kill a Mockingbird, tries to explain to his little daughter why a man just attempt to hurt her and to kill her brother: you must understand, little girl, in this life not everything is beautiful: you must be ready for ugly things.

2) Billy Joel is putting to sleep his little son, and he asks what is death like. Joel is going through a divorce at the precise time and he comes out with this tender and beautiful answer:

http://www.youtube.com/watch?v=LDFBa5tudPk

3) Let me back to A Christmas' Carol and consider the conversion of Ebenezer Scrooge. Would do you not do mockery out of this conversion story? If not, would does it not be possible, from someone else? Would does that mockery not certainly jeopardize the whole ghost tale's message, if so? Dickens, nevertheless, is conscious of it and addresses the question and solve it: "Some people laughed to see the alteration on him, but he let them laugh, and little heeded them; for he was wise enough to know that nothing ever happened on this globe, for good, at which some people did not have their fill of laughter in the outset (...)".

Friday, December 17, 2010

Knock-knock

As usual, it is already late and I push myself to write something, instead of pushing to go to bed. Well, that I will do tomorrow morning, push my self up. So, What can it be to speak about? Mmmmm, there are just to many stupid appreciations to leave here, do not know what to choose. Besides... I was going to say that those comments would be more proper for intimate conversations at the end of the day, but it might be awkward to find your partner in such digressions before going to Nap Land. (I am not sure what direction this blog is taken...). Ok, I will just keep writing, see if the 21-day rule works*.

Well, today I had a beer in the same pub as that I was in on Saturday (where the fox hunters go), right at 6 pm, was bloody cold in London and snowing, and not even one woman _oh, boy, this is becoming a bothersome routine; I took the bus, but drop me in Archway, so I grab the next one and did not pay again for it; I read a friend's borrowed book by Paul Turnier and kind of got cold feet, so you can see our friendship is solid-based. Nevertheless, when I pass on the Westminster Bridge along with some visitor, I know I will tell the story of Boadicea's regarding Boadicea's statue, so I am gaining control over my future actions, a tiny bite to fate's pool of despotism.

What else? In one week, I have seen disturbances provoked by youngsters, chronologically, in London, Rome and Greece, which is another bothersome routine; I tasted again today what bad education is made of; I read last summer Mentiras de Mujeres, by Lyudmila Ulitskaya: Men tend to lie in singular occasions and there is always an objective, but Women lie for no reason and continuously, just lie; I have, however, encounter that Men must find attractive to lie in a very feminine way because some lie just as they breath. It is part of bad education; I find the animal heritage rooted deeply in our bowels. From there, it entreats entrance _Bad education flings wide open the doors to the primitive states of man convivial where all these Gryphons dwell: aggression, untruth and unfaithfulness, selfishness, anxiety.

I read that Black Edwards passed away, which was something about to happen, because Edwards had already received his honorific awards from Cinema Academia. I learn how is the face of Judy Dench or, better, what the name of Judy Dench's face is _Oh, she was so different in the 1970s when doing The Dream of a Midnight's Summer Night! I enjoyed so much the Royal Shakespeare Company's adaptation for Salamanca 2002 in El Liceo; I listened to Martina McBride's In My Daughter's Eyes from an acquaintance who happens to be single mother: never paid attention to the lyrics; Well, McBride has recorded something with The Chieftains, I just noticed; Nice punch I find in Gone, gone, gone, sung by Robert Plant and Alison Krauss; she is too sexy, liquidizer, do you think not? There is this visiting student from Greece who looks to me like Marlee Matlin 30 years ago, same frames and all, and this other student, Chinese-originally, I would say, quite a character. They both went in a funny disagreement and  it came to me: Hm, cat fight!

The piece of news shaking the house was, though, Miley Cirus salvia bong thing. The occurrence pushed Michael Logham to offer fatherly advice to Billy Ray Cyrus, which is another occurrence: an one-eyed man leading the land of the blind.

I have something to say here...I leave it for tomorrow.... Now! Get your ass in bed, dear Albert!

*21-day rule: I heard that anytime you start a new activity, you need 21 days of continuity to have it become a habit. A nonsense.
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(Knock-knock... Is anyone there?)