Dr. Jekyll and Mr. Hyde Contest

Welcome to the fifth annual "Dr. Jekyll and Mr. Hyde" contest. You are each invited to email me a short (1-3 paragraphs) answer to the question: which one of the electric flux (field lines) or electric flow (equipotentials) is more like Dr. Jekyll and which is more like Mr. Hyde? Why? I will post all of your solutions to the course website on the morning of Friday, 2014-10-03.

Your submissions will be "peer-reviewed" by yourselves, under the criteria of physical insight, persuasiveness, cleverness, and humour. Each student may cast one secret vote by Doodle pool, and the winner will be announced during class on Monday, 2014-10-06. First-place prize will be 2% bonus credit in the course, 1.5% for second place, and 1% honorable mention for all submissions.

Fall 2014 Entries:

Entry #1 - tie for First Place

A wise man once said, "We've all got both light and dark inside us. What matters is the part we choose to act on." In the story of Dr. Jekyll and Mr. Hyde, the same man has two personalities, arguably one good the other evil. The man is the sum of his two personalities. Fields also display two different personalities, scalar and vector potentials, which derive the longitudinal and transverse components of a field. If I had to choose which personality of the field is Mr. Hyde, I would choose the flow, which has great potential, just like Mr. Hyde's capacity to do great evil. The flux, on the other hand, is like Dr. Jekyll because it is ready to burst out of him, and become Mr. Hyde, just like the flux through a Gaussian surface. You may not know, however, that there is an extremely rigorous (yet unfortunately obscure) mathematical proof of this comparison. If you assign the corresponding number of the letter of the alphabet to both "FLOW" (6, 12, 15, 23) and "HYDE" (8, 25, 4, 5) then the numbers can be rearranged to obviously show that:

12/6*15-23=7 (Flow)

8-25/5+4=7 (Hyde)

Therefore Hyde=Flow.      Q.E.D.

Entry #2 - tie for First Place

The age-old philosophical notion of duality is readily apparent through all of Nature: sun and moon, light and darkness-and perhaps most prominent of all-good and evil... These ideas date back to the dawn of mankind on this earth. More recently, the dual traits of good and evil are displayed through the ever-popular Dr. Jekyll and Mr. Hyde. Perhaps this duality is so prevalent within the natural world because good and evil is woven inexplicitly into the language of our universe, the mathematics of our world, and the very geometry of the space we live in. Exactly like Dr. Jekyll and Mr. Hyde, the very mathematical fabric of our universe-space itself-exhibits dual properties of good and evil. Space is comprised of lines and of sheets; from these two objects-one of a single dimension and the other of two-one may obtain all the space we know, a three-dimensional sum of its components. But deep within these constituent parts lurks a rising good and evil. The fields within our space are comprised of the good, righteous field lines, but are often shadowed by evil flow surfaces, much like the excellent traits of Mr. Hyde are often hidden under the evil veil of Dr. Jekyll. The field lines of the inhabitants of space represent the direction we must go in order to change our lives for the better and to make our time in space as rich and happy as possible. In doing so, we must power perpendicularly through the evil sheets which overshadow us, just as Mr. Hyde must peel back the many evil layers of Dr. Jekyll to be a happy, civilized man. These sheets of evil surround us at all points, but the only way to most quickly and most efficiently change our lives for the better is to pass right through these sheets in the direction of our lively field lines and into the space and life beyond the evil.

Entry #3 - tie for Second Place

Dr. Crawford,

At times, Dr. Jekyll felt immersed in the flow of the Universe. At every point in space, he was drifting in the ebb and pull of ether. (and although his therapist, Dr. Michelson and Dr. Morley, tell him "Dr. Jekyll, you do know that there is no such thing, right? The ether does not exist!" he persists, shrugging his shoulders and telling them that "Yeah, well, Mr. Maxwell certainly believed and so will I!") It could even be said that Dr. Jekyll was the flow! ... Or was he? Indeed, things that drifted with him did not require any energy to move (the wave would simply carry them)! He was also a man with equipotentials. Figuring out his flow was never too bad, either. Just look at how far he drifts outwards, and away... Ah, yes, Dr. Jekyll really liked being the one to represent least energy ... But there were some things a little off with Dr. Jekyll.

He had a very perpendicular personality. At times, instead of drifting with the flow of the Universe, he would try going the route that spent most of his energy... Piercing straight through the membranes of equipotential. It was like he would go crazy, spouting out that his name was "Mr. Hyde," and that there were such things as ghosts because "spooky actions at a distance" existed everywhere around him! He even claimed he was part of this crazy "action at a distant" theory, but scientists just patted him on his head and said "It could be true, but that would make the mathematics way too hard." (He would often bite their hands after hearing that). Mr. Hyde lusted to create problems in the Universe, but Dr. Gauss persisted on stopping him by trying to get to Mr. Hyde's source by counting how many piercings Mr. Hyde would create over the surface of something that Dr. Gauss would call "A Gaussian Surface."

So you see, Dr. Jekyll and Mr. Hyde are the same and both can represent all fields. White and black together, with different concentrations, creates all shadows, much like flow and flux. What's that, you say? It's a strange concept? Nonsense! Think about it for a while longer and you'll end up coming to the conclusion that there's something perpendicular in all of us. There's no hiding from it, but you are part of this just as much as we are.

Sincerely, Gabriel Utterson

Entry #4 - tied for Second Place

Dr. Jekyll and Mr. Hyde are synonymous in such a way that you cannot have one without the other. In much of the same way you cannot have electric flux without an electric flow, one simply cannot exist without the other. Dr. Jekyll was a charitable man in good standing with the local life which represents in the pair the good side of life. However intrinsically within Dr. Jekyll there was an evil force at work, that work was named Mr. Hyde. Given the nature of the two I would have to say electric flux is more like Mr. Hyde and Dr. Jekyll more like electric flow.

Electric flux is linked with field lines which emanate from a source. Field lines deal directly with the source. Before Dr. Jekyll released Mr. Hyde from within himseH through experimentation, the persona of Mr. Hyde was very much present. Dr. Jekyll had a darker side that was unknown to those around him, that is until Mr. Hyde revealed such natures. Mr. Hyde was very real, in the sense that Dr. Jekyll physically changed into Mr. Hyde. In this same manner Flux gives us an inside to the source, by knowing the field lines, which are as real as Mr. Hyde, We can tell a lot about the source.

Electric flow is strongly correlated with equal-potentials, so surfaces. Equal potentials do not tell us much about the source if just looking at a single equal potential surface; such as it is with Dr. Jekyll. With Dr. Jekyll all that we see is a single potential, that being good. We see his charitable doings and his kindly manner, however looking at this single potential it is unthinkable to suspect that he would be capable of such calibers of evil. That very evil that was ever present. Now again I say both characters represent useful attributes in describing the way things are; such that, you cannot have a Mr. Hyde without a Dr. Jekyll. You could say Mr. Hyde flowed out of Dr. Jekyll. Though If I keep talking like this Ill lose my head like Abraham Van Brunt, which in that case I'd have to start calling you all lchabod Crane.

Entry #5 - tied for First Place

Although human nature has both positive and negative aspects, we are expected to express only the positive. The negative, we project into vices in order to keep them from interfering in our daily lives. Dr. Jekyll is no different. Mr. Hyde is a manifestation for Dr. Jekyll to project his violent urges into. When he becomes Mr. Hyde, he carries out actions without the guilt or fear he otherwise would have experienced. However, each time he returns to himself, he is ever so slightly changed by this experience.

This is similar to the interactions between flux tubes and flow surfaces. Flux tubes project themselves outward, just as Dr. Jekyll projects his negative behaviors into Mr. Hyde. In the same way that Dr. Jekyll turns into Mr. Hyde and returns to himself, when a closed path is traversed, it passes through flow surfaces and returns to its starting point. The value obtained by counting these flow surfaces is different than it was at the beginning, even though it is at the same point in the field. Equivalently, each time Dr. Jekyll returns to himself, he is not the same. Thus it is clear that flux describes Dr. Jekyll just as flow sheets represent Mr. Hyde.



Spring 2014 Entries:

First Place

Flux and flow, yin and yang, good and evil. For eons (or 13.7 billion years, but who's counting..) past, the epic war waged within the fabric of space-time as we know it. To utter the words in Matthew, "Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it. But small is the gate and narrow the road that leads to life, and only a few find it." Clearly the flow, or equipotentials of the electric field is the narrow road, a la Dr. Jekyll. The flow is difficult to find, one needs to first find a charge, and equipped with a voltmeter, determine where these equipotential curves lie. No easy task! Not to mention the tight-rope walk across the line element against the field itself! The flux, or Mr Hyde, is rampant through a gaussian around a charge. Why, all you need is a differential area element dotted with the E field to determine the flux! Clearly, the wide gate is the area differential element, and many (flux lines) are on the path to destruction entering through it! The charge contained is proportional to our flux lines. The tendency for power (or charge) is to become corrupt as it increases. The flux lines are the window to the dark oligarch soul of the massive charges. Snaking it's evil grip across the expanse of space. The flow is our mighty stalwart defender, Jekyllian gradient of justice against these evil Hydian lines absorbing the full frontal attacks! Join with me my brothers and sisters! Stand with Dr Jekyll and the flow of the fields, that will be the road to life.

Second Place

Story of the Source According to the Helmholtz theorem, a man can be broken down into two parts, that which makes him good and that which makes him evil. These decomposed components represent two distinct parts, a vector potential, flux, and a scalar potential, flow, but how can we determine which of these is the representation of a man's evil? In the novella, Strange Case of Dr. Jekyll and Mr. Hyde, Robert Louis Stevenson tells the tale of a man that wishes to vanquish evil from himself, however, this plan backfires causing the evil incarnation, Mr. Hyde, to spring forth. As an analogue to Victorian society, Dr. Jekyll acts as the respectable veneer to the internal brutal-hearted Mr. Hyde. In the Christian religion, we can track evil in man to an original sin, causing the fall from grace. From this point, we can draw an analogy to electromagnetism from the properties stated previously. First of all, the idea of original sin can be drawn to the vector potential, flux. Flux tubes extend from their source and pierce the surface corrupting what was good, just as evil does. The good, flow, can do nothing but count its sins as it counts the flux tubes at the end of sheets, measuring the change in potential. Attempting to vanquish his evil, Dr. Jekyll brought about a greater evil, pride, the greatest sin. By attempting this, he projected his evil onto the citizens of London, something only possible using a vector potential like flux. Furthermore, the attempt to extinguish flux would be an attempt to destroy part of himself, a form of suicide, which denies the gift of life, a great evil from a religious standpoint. Therefore, flux is evil and flow is good, however, we could not fully define a man without both.

Honorable Mention

After considering the dynamic nature of field lines and equipotentials I would say that field lines are more like Dr. Jekyll in that they do not stay in one place and even though they may be constrained in some ways they are constantly spreading into new areas. On the other hand equipotentials are more like Mr. Hyde in that they are stationary though very powerful. While Mr. Hyde is not the type to consider his situation and try to change his lot in life, Dr. Jekyll on the other hand was constantly trying to change is situation with Hyde. Similarly equipotential lines are stationary and do not change while actively restraining other forces whereas field lines describe change in a sense and, instead of restraining forces, can actively push them along.

Honorable Mention

If I had to choose I would make flow Mr. Hyde. Flow is the difference in potential between two points and to quote the Joker from the Dark Knight, "Madness, as you know, is a lot like gravity... all it takes is a little push." After an object is pushed, it may fall and its potential energy will change. This means that Dr. Jekyll will, after a little push, become Mr. Hyde and he represents Jekyll's change of potential.

Honorable Mention

From my extensive knowledge of Dr. Jekyll and Mr. Hyde (and I use extensive here sarcastically because I really learned almost everything I know about them from Wikipedia) I would say Dr. Jekyll would be more like flow, because he flows with society. If he is put into a social situation he will act according to the social norms much like if the closed integral of the flow is taken (in a conservative field like an E field) the integral is zero meaning that just going around a loop didn't change anything much like Dr. Jekyll in the same situation would do the same thing, whereas with Mr. Hyde who knows what would happen if you put him into the same social situation twice. Also Mr. Hyde would be more like flux because flux lines come from a source (a charge), and Mr. Hyde is the source of evilness in Dr. Jekyll and in a sense Mr. Hyde makes the flux lines. Finally Dr. Jekyll and Mr. Hyde are like Flux and Flow because much like how Dr. Jekyll and Mr. Hyde are the different personalities of the same person, flux and flow are different qualities of a field.

2012 Winner:

I do not care for the comparison of Flow and Flux to Dr. Jekyll and Mr. Hyde. Dr. Jekyll and Mr. Hyde are in fact separate states of the same being; the person is merely the superposition of the two that is "forced" into one of the two possible states upon observation (or was already in that particular state just unknown until observation, depending upon whether one holds a realist or orthodox view of quantum mechanics). By comparison, Flow and Flux are geospatial properties that are determined by a common entity (the E-field).

As a thought exercise, I would relate Flow most closely to Mr. Hyde. Dr. Jekyll feared Mr. Hyde's potential, and as we all know Flux fears the potential within Flow when Flow is not bound to a closed path. Flux intends to keep Flow at bay by maintaining a surface with a closed path, and defining a surface which Flux can dominate while keeping the work from Flow at zero. However, Dr. Jekyll felt uncomfortable containing the properties of Mr. Hyde and plotted to occasionally let him out. But the work and potential from Mr. Hyde when not contained to a closed boundary defined by the good doctor frightened Dr. Jekyll.

Lastly, as many may not know, Dr. Jekyll was an ancestor to one Dr. Brown, who harnessed the family's Flux into a capacitor which made time travel possible. As Griffiths likes to say, QED.

2011 Entries:

Entry #1 1st place
Entry #2 2nd place
Entry #3 Honorable mention
Entry #4 3rd place

2010 Winning response:

From Wikipedia: "This idea represents a concept in Western culture, that of the inner conflict of humanity's sense of good and evil. In particular the story has been interpreted as an examination of the duality of human nature (that good and evil exists in all), and that the failure to accept this tension (to accept the evil or shadow side) results in the evil being projected onto others. If someone banishes all evil to the unconscious mind in an attempt to be wholly and completely good, it can result in the development of a Mr Hyde-type aspect to that person's character. This failure to accept the tension of duality is related to Christian theology, where Satan's fall from Heaven is due to his refusal to accept that he is a created being (that he has a dual nature) and is not God."

Conclusion: the flux is Satan (evil). Also, evil can be projected, and since flux is a vector, it can also be projected. :)

Christopher Crawford