Divergent And Convergent Thinking And Their Role Free Writing Sample

Convergent thinking refers to the mental processes involved in generating ideas and solutions to problems. In convergent thinking, the learner uses his/her previous learning and experience to effectively deal with a task or to find solutions to a problem (Atherton, 2005). For example, when a manager is asked to design a program that would increase employee motivation, he would then research how employee motivations are designed and what programs would answer his need. If the manager cannot find anything that is fitted for the company, he proceeds to develop his program but uses his background and knowledge of human motivation and organizational psychology to be able to design an effective program. This approach is similar to the scientific method that most teachers in science adhere to. Although convergent thinking may have been the only form of thinking that we are familiar with, it is however not the only one. Divergent thinking is the opposite of convergent thinking; this refers to the process of finding alternative routes or approaches to generate new ideas and in problem-solving (Atherton, 2005).

In divergent thinking, the learner evaluates the task or the problem as a stimulus that would lead to the solution. The manager who is tasked to develop an employee motivation program would approach the task differently if he was using divergent thinking. In this approach he would see the motivation program as the goal; he would then use the definition of motivation to think of new activities that would answer the need of the company. Divergent thinking does not have set rules and procedures, but rather it is a creative process that would result in innovation.


  1. Atherton, J. (2005) Learning and Teaching: Convergent and Divergent Learning. Retrieved August 25, 2007, from http://www.learningandteaching.info/learning/converge.htm

Convergent And Divergent Nozzle

            A convergent-divergent nozzle, also called De Laval nozzle, CD nozzle or con di nozzle, is a tube that is somewhat pinched in the middle so as to accelerate the flow of gas, which is passing through it. Since the gas flows symmetrically along the nozzle’s axis starting from the inlet to the exhaust, a constriction in the middle will produce a change in pressure and as well as in the velocity in order to satisfy the law of conservation of Energy. As the gas, which emanated from the combustion chamber, enters the nozzle at subsonic velocities (velocity below the speed of sound) with high pressure. As it reaches the nozzle throat it will be contracted down until it reaches sonic velocities. At this point the pressure will be reduced and as the gas leaves the nozzle throat, it will continue to expand and will reach supersonic velocity (velocities above the speed of sound) since the cross sectional area of the nozzle increases. Important considerations in the analysis of gas flow in the CD nozzle includes that the gas is assumed to be ideal, the gas is at constant entropy, there is little amount of heat gained or lost or none at all, the gas flow is constant, the behaviour of the gas flow is compressible, and the mass flow in the nozzle should be sufficient to produce supersonic flow.

            The CD nozzle is commonly located at the end of the combustion chamber and it controls the gas expansion at the exhaust to efficiently convert the energy at the combustion into thrust. By reaching sonic velocities at the nozzle throat, thrust is being produced and carried throughout the rest of the expansion cone. The two major configurations in the CD nozzle are submerged and external. In the submerged type the nozzle entry, the throat, and the exhaust parts are inside the combustion chamber. In the external type, all parts of the CD nozzle are entirely separated from the combustion chamber (see figure 1).

            The CD nozzle consists of three major sections: the convergent section where the subsonic gas flow will be accelerated thus reducing the pressure and increasing its kinetic energy; the throat where it supports the transonic flow; and the divergent section that furthers accelerate the supersonic flow and eventually matching the exit pressure to the outside pressure. If the two pressures do not matched, under a lower outside pressure the CD nozzle will create expansion waves and under a higher outside pressure the CD nozzle will create oblique shock wave.

            A carburettor is a mechanical device that combines or blends fuel and air for an internal combustion engine. The working principle of a carburettor is based on Bernoulli’s theorem that the pressure will be lower if the air moves faster. This principle is similar to CD nozzle wherein a constriction also exists. The carburettor mechanism is actuated by the throttle linkages which controls the flow of air intake to the engine. The speed of which, therefore the pressure, determines the fuel being drawn into the air stream. A venturi type carburettor can either be fixed or variable. In a fixed venturi carburettor fuel flow is being altered by varying air velocity. In the variable venturi carburettor the slide, wherein it simultaneously alters the flow of air, varies the fuel jet opening. A carburettor consists of a “throat” or an open pipe or barrel wherein the air flows through the air inlet of an engine. A venturi form of a pipe is used, a narrowing of the cross sectional area at the middle or a constriction just like in a CD nozzle, to increase the velocity of air coming through it. A throttle valve exists below the venturi to control the airflow, either to restrict or block the air intake. This enables the control of air/fuel mixture inside the system thus regulating the power and speed of the engine. The control of the throttle comes from a mechanical linkage of joints and rods to the accelerator, usually a pedal or an equivalent control of a vehicle or equipment. The fuel is introduced in the system in response to a specific pressure drop in the venturi by means of orifices.

            The nozzle’s throat area refers to the minimum cross sectional area of the constriction in a CD nozzle or in a verturi carburettor. It is in this area where the gas flow gains kinetic energy thus producing supersonic speed after passing through it (see figure 1).

            The Vena contracta is an effect that occurs in air flow through an available opening. To effectively reduce the size of the opening the flowing air “sticks” at the edges of the opening thus reducing the inlet’s capacity to a specific percentage of its size. Though the vena contracta reduces the air inlet capacity it increases the air velocity flowing through.

            Choked flow occurs if the gas velocity, which is travelling through the restriction, tends to increase towards the speed of sound. The choke plane is the physical point where the choking occurs. The downstream pressure will not be a factor with respect to the gas velocity at this point.

            The pressure loss, considering the CD nozzle, occurs at the restriction and eventually causing a higher gas flow velocity. This enabled to increase the kinetic energy of the gas to develop supersonic speed at the throat thus producing thrust at the exhaust section. This thrust is most commonly applied in modern rocket engines and supersonic jet engines.

            Isentropic process is a process wherein the entropy of a working fluid is considered constant. Entropy is a measure on how far the differences in pressure, density, chemical potential, and temperature might exist in the system.

            Isentropic velocity is a condition that is considered reversible and adiabatic. No energy is being added or loss during the flow due to the dissipative effects or friction. In a CD nozzle the ideal gas is at constant entropy and considered adiabatic.

            The flow coefficient is a measure of how efficient a fluid flows. It has a relationship to the pressure drop at the restriction or at the orifice and its equivalent flow rate.


Heldstab, Wayne. The Secret of Super Mileage Carburettors: How they Work and How to Build Them.

Pavlovich, Ivan (1964). Thermodynamics. Western Hemisphere by Mcmillan New York.

Risacher. How to Design, Build, and Test Small Liquid Fuel-Rocket Engines. Retrieved January 29, 2007, from the risacher.org website: http://www.risacher.org/rocket/intro.html

Sutton, George P. (1992). Rocket Propulsion Elements: An Introduction to the Engineering of Rockets, 6th Edition, Wiley-Interscience.

ThinkQuest. Bernoulli’s Principle. Retrieved January 28, 2007, from the ThinkQuest website:


Everything That Rises Must Converge: Meaning Behind The Melancholy

Pour in some white.  Add a little black and mix. The recipe seems simple enough.  In a perfect world, gray would be the harmonious coexistence of the two most contrasting colors on the spectrum.  Somehow these two colors would work together to produce something completely different from themselves, but still a fundamental part of each other.  However, we are not living in a perfect world.  After all, what does the average person see when he thinks of the color gray—rainy days, bullets, fat elephants, rusted and worn metal?  These are not exactly the most pleasant or inspiring thoughts in the world.  Gray is deemed less than desirable by many, due to its cold neutrality.  In fiction, any “gray” work is immediately dismissed with the label of meaningless existentialism.  Society craves meaning and purpose, and it demands these qualities in any written work, so long as those qualities are presented in broad, easily recognized strokes of the pen.  Southern writer Flannery O’Connor did not agree with this philosophy.  This woman’s works have been defined as grotesque, cold, detached, and….meaningless.  The definition could not be more wrong.  In O’Connor’s “Everything That Rises Must Converge,” the complex, yet simple relationship between Julian and his mother serves as a symbolic, hidden commentary into two of the world’s most “meaningful” topics:  socio-cultural politics and religion. “the meaning of a story does not begin except at a depth where adequate motivation and adequate psychology and the various determinations have been exhausted.”—Flannery O’Connor (Galloway, “The Dark Side of the Cross”)

Race relations—and their reflection on human relations—are a cornerstone of the story.

The mother, in all her flamboyant glory, is the perfect symbol of early Southern arrogant innocence (Davie, “Short Story Reviews”).  She views the world in her terms.  The days, for her, are filled with such problems as what hat to wear or how to preserve the Godhigh family name.  Maintaining that name seems very important to her, and she emphatically instructs Julian to act like a Godhigh.  The name carries with it the prestige of old money, and perhaps more importantly, tradition.  It also implies a certain air of moral superiority.  All of these factors basically make up the fabric of who  Julian’s mother is.  The old Southern culture comforts her and gives her a sense of identity (Davie, “Short Story Reviews”).  It is what she grew up in, and it is what she knows.  Yet she seems to filter life’s events through childlike eyes. She seems eternally optimistic regarding her son’s job status.   She assigns an almost comical value to her appearance, worrying over putting up the proper airs for simply going to a meeting.  Also she flutters around as if every event were a grand gala. Her treatment of the blacks provides the best evidence for this view.  The prejudice is ingrained in her.  All of her life, she has known nothing else.  She is fine with the Negroes, as long as they keep their distance.  When the black man boards the bus she is traveling on, she seeks out the opinions of others who will validate her own.  Most key of all, she honestly cannot see how degrading her interaction with the young black child is to his mother. The offered nickel is the final straw.  During the closing moments of the story, Julian’s mother literally gets slapped in the face with the truth, when her blind arrogance ultimately costs her life.

            In stark contrast to his mother, Julian is cynical, angry, vengeful, and “as disenchanted with the world as a man of fifty” (229).  He went to college in the hopes of becoming a writer, yet he is stuck under the label of typewriter salesman.  His anger probably stems a great deal from this assumed job failure, but he also sees injustice in everything around him, especially in the actions of his mother.  Julian does not care about tradition, as he reminds his mother that they live in a broken-down part of town, and angrily proclaims that the family name does not mean anything.  “They don’t care about you,” he insists to her (224).  However, he seems to feel that the family plantation should have been his, which implies a little resentment.  In addition, a critical argument takes place when Julian’s mother claims that culture lies in who one is and where they came from; Julian, in a vehement outburst, tells her that “true culture is in the mind” (227).  He places more value on thought than feeling (Davie, “Short Story Reviews”).  Most of all, he wants to teach his mother a lesson.  He will sit next to a black person, and maybe he will even marry one…as long as they are “respectable” blacks.  Seemingly he is more like his mother than he is willing to admit.  Julian is the face of the changing South:  progressive in thought, regressive in the heart, and locked in uncertainty.

            The conflicted relationship between mother and son provides keen insight into the journey of the South and the force of change.  Julian seems to take delight in antagonizing his mother and brushes off all of the positive things she has done for him (her teeth went crooked so his could be straight).  He seems to totally disregard his heritage.  Yet he would not be the person he was if his mother had not sacrificed for him.  Similarly, the new South arose from decades of tradition and custom, and such things cannot be easily shrugged off.  Ideally, the new would want to take the best qualities from the old and build on them.  Neither mother nor child really understand each other, and seem resistant to even trying (Davie, “Short Story Reviews”).  They are not willing to concede even one inch.  A parallel can be drawn to the white culture and the black culture.  Many whites still make character judgments based on the color of skin, but just as many blacks still harbor a bitter anger towards the entire white race for the years of slavery their ancestors had to endure.  Even today, blacks and whites differ in everything from language “lingo” to hairstyles.  The stroke of the mother signals the end of the story and the beginning of another one (a story with an appropriately undetermined outcome).  In dying, she brings a symbolic end to the old ways.  Julian feels guilt and sorrow because underneath it all, he loves the woman.  In grief and panic, he returns to the comforting word “mama.”  She is his “home,” and home is where the heart is.  The final image of the widened eye is effectively seared into the reader’s conscience.

That bulging eye is the closing image of this story.  But the question remains, is that eye widened in horror, or is that eye finally opened to understanding?  Either way, Julian’s mother realizes that there is no turning back.  Either we plunge ahead blindly and ultimately fall, or we forge a path into a new and better future. Black is not “evil” and white is not “pure,” just as mother and son are not clear-cut good guys or bad guys.  These are only labels that the individual chooses to assign.  Gray is a color of uncertainty, but it is also a color of unity and peace, or should be. Perhaps one day, everything that rises will truly converge into one.  Maybe that ideal is the ultimate hope of this story.

What makes a story work? “some action or a gesture of a character… both totally right and totally unexpected …beyond…any neat allegory that might have been intended or any pat moral categories a reader could make. It would be a gesture which somehow made contact with mystery.” –Flannery O’Connor (Galloway, “The Dark Side of the Cross”)

Flannery O’Connor’s work is often viewed as existential due to her cold and impersonal style and characters (Galloway, “The Dark Side of the Cross”).  Julian certainly fits into this stereotype, with his pessimistic and detached assessments:  “The sky was a dying violet and the houses stood out darkly against it, bulbous liver-colored monstrosities of a uniform ugliness though no two were alike” (225).  However, a closer examination of the plot and characters reveals an intriguing subtext of….spirituality.  Consider the title of the story itself.  “Everything

That Rises Must Converge” is a phrase (taken from a French book) which refers to the Omega Point. And what does this phrase—which O’Connor described as “very stimulating to the imagination”—mean?  The words reference the ideal of a “greater consciousness” between an individual and the world surrounding him, an understanding which leads to Christ (Davie, “Short Story Reviews”).  The first page of the story continues with religious imagery, as Julian envisions himself as Saint Sebastian, “waiting for the arrows to begin piercing him….sacrificed to her pleasure” (225).

 Julian does in fact continue in this martyr/savior role in which he has cast himself (Davies, “Short Story Reviews”).  The sullen young man views the whole bus ride as an opportunity to show his wayward mother the error of her ways.  He unsuccessfully tries to strike up a conversation with the newspaper-wielding black man, and even sits with the man in defiance of his mother.  The man pays him no mind, even assessing him “with annoyance” (230), but Julian’s mind is completely focused on teaching his “red-faced” (230) mother and her gossiping companion a lesson.  He furthers his message by mocking his mother when the black woman (donning the same hat as mother) enters the bus.  He even loosens his tie in mock rebellion.  Julian views his mother as nothing more than a fresh-faced Sunday School child in need of discipline and instruction:  “Two wings of gray hair protruded on either side of her florid face, but her eyes, sky-blue, were as innocent and untouched by experience as they must have been when she was ten” (225).

Yet all of Julian’s righteousness is inherently hypocritical.  He dismisses her childhood dreams of home, yet secretly thinks of the place and its “simple elegance” with “longing” (227).

He angrily rejects her fond memories of Negro servants, whom she’d  “do anything in the world for,” only focusing on her “sins” (227).  He claims to see the affronted African American man and his race “with sympathy,” but “it gave him a certain satisfaction to see injustice in daily operation” (229).  Julian cherishes his moral high ground of righteousness with his mother, but who is truly the more ‘spiritual’ individual?  Is it the ‘boy’ who continuously indulges in an “evil urge to break her spirit,” or the naïve yet simplistic woman (in all her “imagined dignity” glory) who unconditionally defends her beloved, unemployed son against all criticisms and doubts (227)?  Perhaps O’Connor is asking this question of the real world as well, a world where spirituality is either defined by fear-induced rigidity and judgment or by “blind,” loving faith.

Who is truly blind?  Appropriately enough, O’Connor answers this question with an eye:  One eye, large and staring, moved slightly to the left as if it had become unmoored.  The other remained fixed on him, raked his face again, found nothing and closed” (234).  During the final moments of his mother’s life, in Julian her searching eye sees “nothing” (234)….an empty shell where a soul should reside.

“I have found that violence is strangely capable of returning my characters to reality and preparing them to accept their moment of grace…I have found, in short, from reading my own writing, that my subject in fiction is the action of grace in territory held largely by the devil.”— Flannery O’Connor (Galloway, “The Dark Side of the Cross”)

 O’Connor’s fiction often ends with such seemingly random acts of violent death (Galloway, The Dark Side of the Cross”).  On closer examination, however, are these acts so meaningless?  For the human psyche, when do many flashes of clarity or realization arrive?  Do they float in during moments of reflection and peace, as an Emerson or a Thoreau might believe?

Or do they crash upon us without impunity or care, crushing us under their weight?  How often does unbearable loss, or unspeakable circumstance, compel the human mind or stir the human heart?  The whole foundation of Christianity was built upon a horrifically violent act, after all.

O’Connor firmly believed in the concept of Dasein, which views death as the ultimate soul-revealing and  grace-granting experience for a human being (Galloway, “The Dark Side of the Cross”).  Through his mother’s apparent death, Julian displays emotion for the first time.  He experiences “guilt and sorrow” as “Mother!  Mother” suddenly becomes the “Mama!  Mama!” of his childhood (235).  Can this jaded young man find grace?  This is the story’s ultimate question.

Flannery O’Connor has utilized a short tale of a simple bus ride to send a strong message on spirituality.  It is a message utterly devoid of didacticism or preaching, yet it stands as a compelling message nonetheless.  It is a message full of true meaning.       “Prove the truth of the Faith.”—Flannery O’Connor (Galloway, “The Dark Side of the Cross”)

The most fitting evidence of O’Connor’s search for meaning lies in her own life.  The author grew up in the Bible Belt of Georgia.  The influence of her Catholic upbringing is apparent in many of 31 stories and two novels.  In fact O’Connor’s first novel, Wise Blood, possessed an advertising slogan of “A Searching Novel of Sin and Redemption.”  Redemption was a subject which would become even more important to the young Southerner as she battled lupus in the 1950s South.  Crushing symptoms of the deadly blood disease often weighed heavily on O’Connor, and she turned to her writings and reflections as an outlet:  “I can with one eye squinted take it all as a blessing. What you have to measure out, you come to observe more closely, or so I tell myself.”  Fittingly, as with so many of her characters, Flannery O’Connor experienced life through death.  She died in 1955 from lupus complications; she was 34 years old (“Flannery O’Connor,” Books and Writers) . This celebrated Southerner’s legacy lives on in her often “mundane, sometimes laughably pathetic” (Galloway, “The Dark Side of the Cross”) yet always honest, view of the world.

“When the finished work suggests that pertinent actions have been fraudulently manipulated or overlooked or smothered, whatever purposes the writer started out with have already been defeated….[true work will] push its own limits outward toward the limits of mystery.”

–Flannery O’Connor (Galloway, “The Dark Side of the Cross”)


Davie, Patrick.  “Short Story Reviews: ‘Everything That Rises Must Converge.’”  A Student’s

            Guide to Flannery O’Connor.  Copyright 2005.  Accessed October 23, 2006.  Available


“Flannery O’Connor.”  Books and Writers.  Copyright 2003.  Accessed October 23, 2006.

            Available http://www.kirjasto.sci.fi/flannery.htm

Galloway, Patrick.  “The Dark Side of the Cross:  Flannery O’Connor’s Short Fiction.”

Copyright 1996.  Available http://www.cyberpat.com/essays/flan.html

O’Connor, Flannery.  “Everything That Rises Must Converge.”  Growing Up in the South.

            Suzanne Jones, ed.  New York:  Signet Classics, 2003.

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