A Most Excellent and Scholarly Investigation Into the Essence Of

A Most Excellent And Scholarly Investigation Into The Essence Of Don Todd Hereby published as the culmination of the laborious studies of Sir Alan Berger and Emperor Hahn Rah Introduction

The central problem to this study arises as follows: a group of exceptional physics students are intently following the lecture of Mr. Jeffrey Wetherhold. The lesson focuses on applications of integration in mechanics. As the letters dt, representing an infinitesimally small interval of time, keep resurfacing, three students take particular interest. Todd Mueller, one of the men in question, goes by the nickname Don Todd. This is often abbreviated dt. The other two, Matthew Hahn and Alan Berger, are perplexed by the inextricable tie between Todd’s nickname and a mathematical symbol. Their inquisitive spirit leads them to ponder the obvious dilemma: whether or not the letters dt are merely coincidence. To discover if Todd’s name can be integrated, they embark on a quest of epic significance. They devote themselves to an exhaustive research project with the goal of integrating Todd’s nickname. To accomplish this feat, they bridged the dichotomy of science and linguistics. The relative speed and astounding accuracy of this technique provides infallible proof that this method has always existed but simply has never been explored. An explanation of this procedure combining science and English follows. The founders have labeled the process the calculus of the English Language.

The Calculus of the English Language

The calculus is a powerful problem solving tool. As the omnipresent voice in the Mechanical Universe videodisk declares, the calculus is far superior. When, however, the individual wishes to apply these methods in unconventional ways, a broad understanding of the fundamental concepts that are central to the calculus becomes indispensable. The following entries will whet one’s appetite, but they are far from complete and serve only as background material. The developers of this process recommend further research to anyone unfamiliar with the multifarious idiosyncrasies of the calculus.

The Derivative

The derivative is the cornerstone of the calculus. The general concept of the derivative involves rates of change. Given a function f(x), the derivative f’(x) is a new function which is equal to the rate of change of f(x) at each value of x. In other words, f’(x) is the slope of f(x). Because slope is change in y divided by change in x, the most commonly accepted notation for a derivative is dy/dx, where dy represents an infinitesimally small change in y and dx represents an infinitesimally small change in x. There are a plethora of mathematical processes for deriving these new functions from any number of original functions. Another name for finding the derivative is differentiating. Generally, differentiating will produce a more simplified function of a lower order.

The Anti-Derivative

As the name implies, the anti-derivative is a derivative done in reverse order. The mathematical process is also called integration. When integrating the function f(x), the goal is to find a function F(x) whose derivative is f(x). This new function F(x) is the integral of f(x). While the derivative f’(x) measures the slope at each point of the function f(x), the anti-derivative F(x) measures the area beneath the curve f(x). The area is a summation of many rectangles. These rectangles have a height equal to the value of the function f(x) and a width dx. The integration sign is an elongated s, and it simply denotes a summation of these many rectangles. The most common notation for an integral is ∫f(x)dx. This arises from the formula for the area of a rectangle. Note the two dimensions f(x) and dx are multiplied together. Then integral sign notes that all these rectangles are summed together. The processes of differentiation and anti-differentiation are inextricably bound together. Taking an integral will produce a function whose derivative will reproduce the original function. In the language of the calculus:

d/dx [∫f(x)dx] = f(x)

Again, there are a multitude of mathematical formulas achieving these new functions through integration. The integral generally produces a more complex function of a higher order. One important note is that functions represent graphs. Given a function, one can determine a definite slope at any point. Because the slope is definite, there is only one derivative from a given function. However, the anti-derivative is different. From a function one can find the area under the curve only if definite bounds are set on the function. It is possible to note the change in the anti-derivative, but the starting point is arbitrary. In other words, the only definite is the change in the function, or its slope. Thus it is possible to determine the shape of an integrated function, but more information is necessary to pinpoint its exact location along the y-axis. To note that these infinite possibilities exist, the integrated function ends with a constant, C. This makes perfect sense because when the derivative is taken, the constant drops out and the original function remains, whether the number was 0, 42, or any random digit. Both the derivative and the anti-derivative more fully describe a function. A derivative will reveal any small change whereas an integral will deliver the area. This area concept seemingly fills out the function, achieving its true essence. With this background knowledge, the processes will now transcend the traditional boundaries of mathematics. The remainder of this proof will explain and utilize the calculus of the English language.

The Derivative in the English Language

The process of differentiating produces a function that is derived from the original. It is possible to have many functions that are all derived from the same original equation. In the same way, words are derived from each other. This is prevalent in the use of nicknames, where a variety of substitutes are derived from the original name. However, this process does not simply apply to names. Lower order words can be derived from higher order words in the same manner as equations of low degree can be derived from equations of comparatively high degree. For example, an object that is perfect cannot be improved upon. Therefore, all adjectives describing a general positive quality are derivatives of the word perfect. For instance, the term godlike describes an object that is nearly perfect. It is the first derivative of perfect. Subsequent derivatives form a ranking of these positive words from perfect down to good. A listing of perfect and its derivatives follows. Table 1.1

Derivative Adjective - Perfect 1 Godlike 2 Supreme 3 Awesome 4 Glorious 5 Magnificent 6 Spectacular 7 Outstanding 8 Wonderful 9 Fantastic 10 Splendid 11 Excellent 12 Super 13 Grand 14 Great 15 Good

The order and completeness of the list are assuredly perfect because Matthew Hahn, the epitome of perfection, has decreed that it is so.

The Anti-Derivative in the English Language

In the same manner, it is possible to apply the general principles of anti-differentiating to words. This process provides a fuller meaning to the word in the same way that finding the area under a curve does. It regresses to the root of the word, revealing from whence it has come. The key for integrating any word in the English language is to decide from what it has been derived. A child is derived from parents, so it follows that the integral of child is parent. The same applies to the masculine and feminine counterparts, with the integral of son equaling father and the integral of daughter equaling mother. Using these analytical techniques and a wealth of ingenuity, it is possible to integrate and differentiate words as well as numbers. Henceforth, the next segment of this document shall contain the steps leading to the discovery of the answer to the primary objective: determining the essence of Don Todd by integrating his nickname. The Nickname

Todd Mueller’s nicknames characterize his multiple personalities. One of his most prominent personality traits is his suave behavior around the feminine gender. After a lengthy examination stage, conclusive evidence exists that Todd cannot survive long periods of time without at least two girls at his side. The following witnesses affirm the validity of this statement by having participated in the period of scientific observation.

I do hereby attest to the fact that Todd Mueller constantly seeks the presence of women regardless of his location. I have observed this phenomenon with multiple women. I have noticed these tendencies on my own and have come to the conclusion that Todd Mueller is a player. I do solemnly swear to the validity of this statement upon my sacred honor.

(This page was completely filled with the signatures of qualified observers. A scanned copy of the original page may be included in the future) Indeed, Todd cannot be satisfied with one girl. At school dances, he has been observed to supplement his dates with additional young women. He exhibits shameless flirtation at any given time and place, even during physical education. Todd’s charming tendencies and pandering nature merit the prefix Don to be used before his name. This addition stems partly from the romantic exploits of Don Juan and also from the picaresque adventures of Don Quixote. However, Don Todd is not the only pseudonym for the infamous Todd Mueller. In elite circles, his complete alias is “Numba one playa supa pimp masta mac daddy t dogg.” Todd’s proclivity toward women necessitates the thematic repetition of words pertaining to a philanderer. Empirical evidence supports the fact that Todd is, indeed, a player. The well noted Jewish scholar Joshua Bergstein states in his essay entitled “The Wigger Genocide” that driving “a pimped-out Honda Civic” is an essential characteristic of a player1. Not coincidentally, Todd drives a blue Civic. In support of this view of Todd, a file of pictorial evidence has been assimilated and shall be included in support of this document. A cameraman wishing to remain anonymous captured the shots during a physics class excursion to Dorney Park. Accompanying the incriminating photographs are a few other pieces of relevant information. One is a list of names found underneath Todd’s desk in health class. Experts have determined that this list indicates his intended affairs for the weekend. (These elements are lacking in this document, but scanned copies may be added after an indeterminate time interval)

Final Introductory Notes

To this point, the authors have introduced Todd, his nickname, and the circumstances surrounding the nickname. Irreproachable proof exists to validate the use of this nickname for a character such as Todd. The authors have presented the calculus of the English Language as a valid method of analysis. Intuitively, the procedures prove themselves to be true. Although further assurance is unnecessary, the imperial Hahn dynasty proclaims the authenticity and accuracy of these methods now and henceforth.

1 Bergstein, Joshua. “The Wigger Genocide.” Hoboken: Dead Baby, 2003. A copy can be found in the cache of additional evidence at the end of this document. With these relationships firmly established, the next section will take the given information and use the calculus of the English language to burrow deep within Don Todd’s aura of mystique in order to extract his true essence. The following section is the heart of the project, the fruits of extensive thought and labor. The Integration of the Nickname

Start with Todd’s nickname. It is a derivative of Todd’s original name, which will be abbreviated with a capital T. dT/dt = numba one playa supa pimp masta mac daddy t dogg (1)

Multiply both sides by dt. dT = (numba one playa supa pimp masta mac daddy t dogg)dt (2)

Integrate both sides.

∫dT = ∫(numba one playa supa pimp masta mac daddy t dogg)dt (3)

T = ∫(numba one playa supa pimp masta mac daddy t dogg)dt (4)

These primary steps have proven the obvious: that Todd is equivalent to the integral of his nickname. This makes perfect logical sense. The nickname, because it was derived from the original name, should be equivalent to the latter when integrated. The following steps will use the Calculus of the English Language to integrate the right hand side of the equation and reveal Todd’s true essence.

Move constants through the integral sign.

T = numba one ∫(playa supa pimp masta mac daddy t dogg)dt (5)

Playa is the Spanish word for beach. It is derived from a Spanish beach. Therefore, the integral of a playa is a Spanish beach. In the language of the Calculus:

∫(playa)dt = Spanish beach (6) The constant is ignored here because the integration is not yet complete. Insertion of the constant will be postponed until the final portion of the integral has been conquered.

Substitute:

T = numba one Spanish beach ∫(supa pimp masta mac daddy t dogg)dt (7)

Supa is a term from Ebonics equivalent to the English word super. Using Table 1.1 from the preliminary explanation:

∫(super)dt = excellent (8)

…and, thus…

∫(supa)dt = excellent (9)

Substitute:

T = numba one Spanish beach excellent ∫(pimp masta mac daddy t dogg)dt (10)

To find the integral of a pimp, it is necessary to consider from what a pimp is derived. Conclusively, any philanderer must have loose moral values. This weak set of principles results from a corrupting influence. However, the word pimp also implies a high class standard. Many modern pimps in the rap industry drive flashy cars, wear bling-bling and ice, and prefer precious metals to teeth. The existence of these decadent tastes necessitates the use of a well-written expression for the word corruption. James Joyce as an author is comparable to Mercedes as an automobile manufacturer. The names both embody critical acclaim. Joyce’s renowned style matches the distinction of a Mercedes logo on the hood of a vehicle. Henceforth: it is proper to use a quote from James Joyce about corruption rather than simply state the word corruption itself. The embellished phrase can be found in Joyce’s Portrait of the Artist as a Young Man. It reads, “jellylike mass of liquid corruption” (128). Using this knowledge, it follows:

∫(pimp)dt = jellylike mass of liquid corruption (11)

Substitute: T = numba one Spanish beach excellent jellylike mass of liquid corruption ∫(masta mac daddy t dogg)dt (12)

Masta is another Ebonics term which stands for master. A master is derived from self interest. If no person wanted to seize power for himself, there would be no masters in this world. Intuitively, people are motivated by self interest because some have claimed predominance over others. In this manner, a master is the derivative of man’s innate egoistical propensity. Therefore, a masta is derived from the same essence.

∫(masta)dt = egoistical propensity (13)

Substitute:

T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity ∫(mac daddy t dogg)dt (14)

The prefix Mac, traced to its Irish roots, implies a patronymic relationship. When affixed to the front of a surname, the word denotes that the owner of this name is a son of the aforementioned family name. Clearly, this term deals with genealogy. It is necessary to determine whether Don Todd’s lineage is aristocratic, common, tainted, or any other of a number of adjectives. After extensive historical research, Todd’s family tree can be drawn as shown on the next page. Chart 1.2 GENEAOLOGICAL REASEARCH

G1 Don Quixote Dulcinea FEMALE DATA NOT AVAILABLE G1 (in this era female lineage G1 was considered unimportant, G1 thus historians kept limited records) G2 Diego Laínez Doña Teresa Núñez a G1 G1 G1

G3 El Cid (Rodrigo Diaz) Doña Jimena a G1 G1 G1 G4 Don Pedro Doña Magdalena G1 G1 G1

G5 Don Juan (mother unknown, multiple possibilities) G1 G1 (lost generations) G1 G1 G1 GX Alfred Mueller Janet Mueller Bill Ryan Helen Ryan G1 G1 G1 GY Rick Mueller Nancy Mueller G1 G1 G1

GZ Todd Mueller Taryn Mueller

Notes: Persons of note appear in bold script. Don Quixote was conceived from an idea, not a person. Hence, the line can extend no further into the past as no physical ancestors exist. Unavailable data from maternal side and lost generations is immaterial. Generation count appears on side. The accuracy of the research represented in this chart is guaranteed by the Hahn Dynasty. Chart 1.2 proves that Don Todd is a direct descendent of Don Quixote. Cervantes created this character to epitomize the romantic sojourner, destined to wander the countryside in search of his true love, Dulcinea. Referencing the fact that Don Quixote did not actually exist (rather, he is a popular element of folklore), one can conclude that Don Todd is of mythical lineage. However, Todd also shares the same bloodline as El Cid. This champion of Spanish culture proves that Don Todd is indeed of noble lineage. To verify that this series is definite and convergent requires the use of the Ratio Test. Again, this involves a new concept from the calculus and can be researched accordingly.

Ascending Todd’s family tree in the direction of the past, it becomes evident that the characters have increasing elements of myth. Don Quixote, as a character from a fantasy novel, has greater mythical elements than his descendents. Those descendents, El Cid’s parents, were among the nobility of Spain. It follows that when examining a pair of terms high in Don Todd’s family tree, the higher of the two will be more mythical, while the lower of the two will be more noble.

Lim an+1 mythical n  ∞ an noble

Comparing the relative importance of the two words, it is evident that nobility supercedes mythology. The word has more strength; it is rooted in a concrete concept rather than grasping for an abstract thought. As n approaches infinity, the potency of the word noble in the denominator causes the fraction to approach 0.

Lim mythical n  ∞ noble

This result proves two things. Nobility precedes mythology when describing Todd’s lineage. In addition, Todd’s ancestry is convergent. It is defined and real.

Unsurprisingly, Don Todd shares the ancestral blood of Don Juan, a noted womanizer. This serves to confirm any and all conclusions made in this proof. Because the word mac is derived from Todd’s lineage, the integral indubitably reflects his legendary heritage.

∫(mac)dt = noble lineage (15)

Substitute: T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage ∫(daddy t dogg)dt (16) The next word presents perhaps the most simple of the terms for integration. A daddy, when ascended one level, becomes a granddaddy. Daddies are derived from granddaddies. The analogy is clear, simple, and irrefutable.

∫(daddy)dt = granddaddy (17)

Substitute:

T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy ∫(t dogg)dt (18)

Any student of moderate proficiency with the tools of the calculus can perform the next function. The integral of the parameter t with respect to itself becomes t 2/2. Skeptics may reference any respectable book written on the calculus. More preferably, one might seek enlightenment from Mr. Charles Merlo. Before he retired, this mathematical wizard could always be found instructing students of the calculus at Parkland High School in room B112. Although he can no longer be found there, both the researchers of this project highly recommend a pilgrimage to his former instructive chamber2. From there it may be possible to reach enlightenment through osmosis, absorbing the residual brain energy which Merlo has undoubtedly left behind. Another presumable benefit of such a trip would be to glean his current location from any member of the office staff. Merlo would verify that the integral of t with respect to itself is t2/2.

∫(t)dt = t2/2 (19)

Substitute:

2 Parkland High School 2700 N. Cedar Crest Blvd. Allentown, PA 18104 United States of America (See end notes for schematic diagram leading to B112.) T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy t2/2 ∫(dogg)dt (20)

The final term to be integrated is dogg, another Ebonics term. As one might imagine, it refers to the mammal commonly known as a dog. The first domestic dogs came from the wild. At one time, they were wolves in the enchanted forests of Norway. Therefore, the integral of a dog, and also a dogg, is a wolf. ∫(dogg)dt = wolf (21)

Substitute, remembering to add the constant of integration as this is the final term to be integrated:

T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy t2/2 wolf + C (22)

To determine the constant, knowledge of an initial value is necessary. The variable t traditionally stands for time. At the beginning of time, Todd did not exist. This means that when t = 0, T = 0. Substitute this knowledge into the previous equation:

0 = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy (0)2/2 wolf + C (23)

0 = C (24)

The constant can be eliminated from the equation. The final result is as shown:

T = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy t2/2 wolf (25)

These sacred words depict the true essence of Don Todd, a portrait of a young gentleman with a Spanish flair that allows him ease of passage with his female relations. However, this outer ego only serves to mask the true corruption inside of him. His self motivation rages from the carnal desires of an untamed animal. Despite this youthful playfulness, he maintains the respectability and poise of a dignified grandparent. Undoubtedly, this proof has been an accurate insight into Todd’s personality.

In the language of the calculus,

∫(numba one playa supa pimp masta mac daddy t dogg)dt = numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy t2/2 wolf

Or, in simple English,

He is a numba one Spanish beach excellent jellylike mass of liquid corruption egoistical propensity of noble lineage granddaddy t2/2 wolf. END NOTES

The authors of this proof suggest using the Calculus of the English Language to discover the inner self as a viable alternative to suffering a pilgrimage such as the one described in Hesse’s Siddhartha.

Acknowledgements:

*Mr. Jason Lerew, band director at Parkland High School, for permitting endeavors far more important than practicing in his practice rooms

*Mr. Charles Merlo, for so skillfully watering the seeds of budding mathematicians

*Mr. Charles Tannery, for letting his English students do almost anything, as long as they did something

*All the participants in our scientific observation period, thank you for your hard work and diligence Floor Plan -- Parkland High School

Enter at the middle of the central arc underneath the large concrete sign which reads “Academics.” Continue along the first story as noted with the yellow line. Yellow star denotes room B112, the instructional facility previously graced by the presence of Mr. Charles Merlo. The Wigger Genocide by Joshua Bergstein

Our status quo is not all “up in here, yo.” We gots to put some shizzle in dat nizzle to fix the mofo up. Word.

Wiggerism, much like Scientology or Exploding Man Syndrome, is a black plague, or should I say white plague, on society. At least five times a day, my eardrums are pulverized by rhythmic bass coming out of some crappy import car, while a “professional” generic rapper speaks of hoez in his hizzouse. I then look past all the bling-blingin’ (read: retina damaging) chrome to see some really cool kid bobbing his head up and down with the beat. You can tell he’s really cool, because he is wearing a visor upside down AND backwards. For those of you keeping track, that’s 80lbs. of cool per square foot (in the metric system, I believe that’s 88.72 hectameters per cubit). This kid is also white, even though the glare from the chrome scientifically should have taken off the top three layers of the epidermis. Behold, I have found a wigger.

Let’s start with some history. Wiggerism started with the advent of Vanilla Ice, back in 1898. He got off the boat from some country far away (who hopefully we have nuked by now), and tried to bring about change in the good ol’ US of A. Mr. Ice (not to be confused with Ice T, who is not to be confused with Mr. T), noted that people were not getting “down n’ dirty” enough. Wiggerism started as a small cult on a farm in Ohio. It caught on like wildfire in an orphanage made out of cardboard, and was known nationwide by the 1920’s. Contrary to popular belief, Coolidge was not a wigger, although FDR did convert to it in the middle of his term, and was known to ride around in his wheelchair in a very slouched-down manner. Wiggerism reached its heyday during World War II, when troops would lift each other’s spirits by somehow adding Honda Civics and crazy gumby gold into their daily march litanies. These infectious stanzas even caught on with the Germans, eventually leading to the creation of a group of rapper/soldiers named Da 3RD Reich Yo!

Today, Wiggerism is a multi-national conglomerate, appealing to the non-blacks of anywhere who feel the need to rebel because their “whack” momma made them feed and walk the dog. It is an angry outlet for those who suffer from the white-boy, middle class pains. They are able to fancifully “bust a cap” and “get down with some hoez.”

Wiggerism must end. It was novelty for a short time, but now I feel a pressing need to stroll down to the MTV studios with dynamite strapped to my chest if they play anything with Ja Rule ever again. They are a sub-culture whose very existence should be questioned, and then shot at with antiaircraft missiles. Not only have they severely bastardized the English language, they have bastardized the already bastardized English the modern rappers use. I refuse to have my generation degraded even further by these chrome-loving suburban rebels. I will listen to music that actually means something, and not take off my clothes just for the sole purpose that it is indeed “hot in here.” I WILL NOT classify The Fast and the Furious as a real piece of cinematic work, and I WILL NEVER drive a “pimped-out- Honda Civic. You down with all this shizzle?