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