Sunday, November 3, 2013

The Roller Coaster Lab and Chaos Theory

Last week, I ran a lab with Honors and AP where they were to design a roller coaster track for a marble to travel down.  The coaster had to have a bunch of little things, such as a loop, a jump, a couple of hills, and it had to land in a cup.  I gave each group 3 tries to sink the marble.  Most groups made it at least once, but few made it more than once.  We may ask "How did we not obtain the same result each time?"

Scientists assume that each trial in an experiment was done in a manner that changed no more than 1 variable.  Otherwise, changing more than 1 variable could result in a change as a result of 2 changes, neither of which can be separated by itself.  The goal is to separate exactly 1 variable, so everything else must be done exactly the same.

Try doing this.  Try dropping a bouncy ball from the height of your head.  Record the location of the third bounce on the floor.  Now try doing the exact same thing to achieve the exact same result.  It's harder than you think.  The ball and floor have all kinds of hidden variables that we can't measure, such as irregularities in the surface of the ball, slight .001 degree tilt of the floor, or inconsistencies in the amount of air resistance encountered as it falls.

In our lab, we dropped the marble, and for the most part, nobody made any real changes in the design from trial to trial.  Some groups moved the cup; others tweaked the track a bit, but most, if not all, groups, experienced some variation from trial to trial, despite making no changes.  We may ask how this could have happened.

Suppose you dropped the marble a few millimeters away from the starting point.  This would slightly change the amount of initial potential energy, changing the kinetic energy at future points in the coaster.  At some points, that change can be enough to cause the marble to hit an uneven bump in the track, causing a variation in the amount of friction encountered.

Another possibility is that you put some sort of spin on the marble.  You will learn that a spinning object has "rotational kinetic energy," which adds to the total energy of the marble.  This slight change can create a major change later on in the coaster.

Chaos theory states that changing one tiny, seemingly insignificant detail can lead to a series of increasingly noticeable changes that eventually change a final result.  An example of this is in Ray Bradbury's short story, A Sound of Thunder.  A hunter who travels back in time accidentally steps on a butterfly, changing things, such as how words are spelled or how people support politicians.  Although we might find this example to be a bit of a stretch, the idea is quite sound.

Killing one butterfly means slightly less prey for a natural predator.  Maybe an animal needed that butterfly to make the difference between survival and death of itself.  Perhaps such animal would have given birth to more species, one of which could have had a necessary mutation to evolve into a modern species that we humans encounter.

Perhaps this species influences our culture or behavior by affecting our ecosystem, killing unwanted disease-ridden animals, or by controlling the population of a disliked animal.  Maybe the politician that a person would have supported had a position regarding how to handle the population of a species that no longer exists all because a guy stepped on a butterfly.  Hence, chaos theory (sometimes called the butterfly effect; Bradbury did not invent the term, he used a butterfly to make reference to the term).

I'm interested in hearing about other possible changes that could have caused the marble to behave differently.

Wednesday, October 30, 2013

"Evolution is only a Theory" and misconceptions about science.

Her name is Amanda.  She is a wonderful character, with great moral values.  She and I always enjoyed talking at the dinner table in college; we'd laugh about whatever was going on around us, we were both forensic science majors (before I switched majors); both of us were taking biology, and she usually has a great deal of common sense.  Despite our friendship, we always differed on just about every debatable topic.  She is pro-life; I am pro-choice.  She was for capital punishment; I am vehemently opposed to it.  She puts an inordinate amount of faith in the Bible; I view it as a trivial work of fiction.  Needless to say, she believes in Creationism; I believe that we are products of evolution.

We always got into arguments at the dinner table.  We remained friends, but we always got into arguments.  The one thing that I could never get over was that she was a forensic science major and rejected any piece of science that conflicted with the old testament.  She always tells me that "Evolution is only a Theory;" this is what kills me.

"Evolution is only a theory."  Many fundamentalists chant that mantra when they want to protect their views. I find myself fuming on the inside when I hear this. You can believe in your religion and accept evolution simultaneously; they often do not conflict, but no scientifically literate individual would willingly state the above mantra.

Most of us, when we hear the word theory, think of a proposed idea with insufficient knowledge to be considered valid.   Dictionary.com defines a theory as:

Theory - a coherent group of tested general propositions, commonly regarded as correct, that can
 be used as principles of explanation and prediction for a class of phenomena:

A theory is actually a very high degree of confidence.  The reason why evolution is a theory and not a law is that there is no way to experimentally prove this.  Evolution takes too much time and depends on variables that cannot be independently manipulated.  Imagine trying to design an experiment to prove evolution; you can't!  This is why evolution is "only" a theory; the quotation marks parody the fact that all scientific theories are very well established.

This is in contrast to a law, which is an idea that has been thoroughly tested and found to have stood strong despite several attempts to "foil" such principle.  Scientists are really designing experiments in an effort to disprove their hypothesis.  This is why a law is the most powerful degree of certainty in science.

So, where do we have absolute truth in science?  We don't.  Well, sort of.  We could state that it is absolutely true that 3 is a prime number, or that adding 2 jelly beans to 3 jelly beans yields 5 jelly beans, but these are rules of mathematics, which is really science without the tangible world.  Once you add the physical universe, you can no longer state that you are "absolutely certain" about something; this concept doesn't exist.

Gravity, currently a law, was once a theory.  It remained a theory until Henry Cavendish created a device that could determine the universal Gravitational constant, G, which equals 6.67 x 10^-11 Nm^2/kg^2.  It is possible that one day, gravity will be replaced by an even better explanation.  Nobody currently knows why gravity exists; we only know how it exists.

On the scale of scientific certainty, the most basic level is a paradigm.  A paradigm is a proposed, highly uncertain model, or explanation of how something works.  Aristotle's explanation of how the universe worked was a paradigm; it had no real proof, other than a few inert, incomplete observations about how things always "seek rest."  He was absolutely wrong on that matter.

After a paradigm is a hypothesis, which is an announced, educated proposal.  Some call it an educated guess, but a hypothesis is better than this.  Evolution does not contain a real "hypothesis" because it cannot be tested.  A theory occurs when instead of directly testing a hypothesis, people make observations related to the idea, all of which seem to support it.  Not all scientists have to definitively agree on a theory; but most should.

Where does creationism or intelligent design fit on this spectrum?  Think for yourself on this one.  I don't think there will ever be true scientific support for creationism, since evolution can consistently explain what creationism cannot.  Evolution does not ever have to become a law; a theory remains valid until a better explanation is reached; the only way to "kill" an idea is with a better idea.

My conclusion:  Evolution may only be a theory, but on the same scale, creationism is not even that.  I am not telling people to drop their religion; I have many Jewish and Christian friends who accept evolution over creationism, so there is no reason why you cannot have your cake and eat it, too.

The Hunger Games and Quantum Physics

Early in 2012, I, along with a friend of mine and his girlfriend decided to drive out to Sandusky, OH to meet up with a college friend of hers.  The four of us decided to see The Hunger Games on opening night.  I never read the book, nor did I really know anything about the story, but I quickly took note of the post-war dystopia in which such people lived.  I analyzed the movie from a physics perspective, and tried to analyze how I would have played the game, if put in such situation.

The analysis I used was that of a quantum physicist.  Quantum physics is the study of energy states of tiny particles.  An electron can have an angular momentum, or a magnetic spin number of either + 1/2 or -1/2.  The actual energy it has would be either ħ/2 or -ħ/2, where ħ is a constant related to Planck's constant.  The important thing to understand is that an electron can either spin clockwise or counterclockwise.  An individual electron is difficult to anticipate, since it has a 50% chance of spinning in either direction.  A large amount of electrons can be assumed to have an expectation value of 0 angular momentum, meaning that the positives and negatives cancel out.  It is nearly impossible to know the energy of one individual electron, so we may think that quantum physics is useless... Or is it?

Upon hearing your name called, you know nothing about your competition, so you assume that you are as likely to survive as anybody entering this game, giving you a 1/24 probability of survival.  You may consider yourself dead... or just a wee bit alive.

Quantum physicists say that you are BOTH alive AND dead before the game occurs.  More specifically:  you are 23/24 dead and 1/24 alive SIMULTANEOUSLY.  This is how Schrodinger described a cat placed in a box of poison.  Unless we actually look to see what's inside, the cat is both alive and dead (why would somebody want to do this?).  Upon making a quantum measurement, or in this case, looking at the cat, you can now conclude with 100% certainty what state something is in.

All quantum states must quantified and describable to a degree of direction.  This means that Katniss is 1/24[A] and 23/24 [-A]:  [A] stands for alive, where [-A] stands for negative alive, or dead.  When writing a formal quantum state, we actually use the square root of the probability, and this is used for a certain reason (I won't go into detail).

Thus:  [K] = .204[A] + .979[-A]

The coefficients are the square root of the probability of each state, in decimal form.
This is how quantum energy states are described.

Upon learning new information about one's rating compared to other tributes, you can alter a quantum state by determining a more accurate probability.  Quantum physicists do this whenever they develop further research.  One might say that Katniss did not improve her odds; she was always good with a bow, and likely to survive, but a fundamental principle of quantum mechanics is:

AN OBJECT'S CHARACTERISTICS DEPEND ON THE OBSERVER'S KNOWLEDGE AT THAT TIME.

This is starkly in contrast to what 90% of science experts think.  This is not to say that they are dumb; quantum physics is a very recent field of study; only around for a bit over 100 years, and much is still unknown.  For most of science, it is safe to assume that something is what it is without human measurement.  However, quantum physics governs everything in science, so keep in mind the importance of human perception.

Quantum states change all of the time.  The only states that don't change are called "eigenstates."  I think eigen is German for "own."  Perhaps that could be twisted to mean that the state remains as its "own" and is not affected by time.

Another major thing to understand about quantum physics is that:

UNTIL A MEASUREMENT IS MADE, QUANTUM STATES CAN ONLY BE EXPRESSED IN TERMS OF PROBABILITIES.

Suppose Katniss died in the beginning.  Upon receiving the information of the cannon firing on her behalf, she would then be in the state of:

[K] = 0[A] + 1[-A].

Every time somebody dies, Katniss's quantum state changes.  She is now more likely to live, so the state weights itself towards the [A] state.

This means that if you enter the hunger games, no matter how dominant you may seem to be, your best bet is to avoid confrontation for as long as possible, because every time you enter a confrontation, there is a probability that you will not survive it, so your chance of survival is greatly enhanced by curling up under a bunch of rocks and eating leaves.  After trying to determine how to engineer a superweapon out of the environment, I concluded that the theoretical physicist has the ultimate advantage in doing nothing.

I would have either done the above or attempt to fake my death.

One last question:  let's see how well you understand quantum physics.  Suppose I play a hand of poker, and without knowing the value of any cards but my own, I decide to "burn" 2 cards instead of the customary 1 card prior to dealing.  Did I change the game?  Somebody who understands quantum physics knows the answer.

Thursday, October 17, 2013

Modern Issues that Arise with Colleges

In the colonial era, people in Great Britain desperately wanted to move to the 13 colonies because of the opportunity that arose from such land.  In order to raise the economic means to do so, they were required to dedicate 7 years of their life to being an "indentured servant" in which they had to work for a rich person, who after 7 years, would compensate them by paying for the voyage across the Atlantic, and giving them money in return.

College has become this system, only backwards.  You spend the best 4 years of your life in an environment where you are free to say whatever you like.  People are as relaxed in judging others as they will ever be. Mostly everybody is popular in college.  There's no "mainstream" clique; you can find a group of friends as a seemingly endless list of common interests link people all across the campus.  There is a reason why you seldom hear of college shootings; the culture is far more open and accepting, and society is not that way in high school, or after high school.  It is not until later that you will have to pay it all back.

The actual amount of time you spend in classes is quite minimal.  This leaves you with all kinds of time to kill, by either doing homework that is often not even checked, reading, going out and enriching yourself in the arts, or going out and making bad decisions.  Everybody in college knows somebody who makes bad decisions, and you know what I mean.  Part of developing in life is learning from mistakes.  My motto is that life is not about learning from your mistakes; it is about learning from the mistakes of others.  I stayed away from most parties, and I learned from others about safe vs unsafe party behavior.  I learned from my buddies who started smoking about how nasty it is, the smoker's hack, and the economic cost of smoking.  I have never smoked a cigarette in my life, and I plan on keeping it that way.

Despite the enrichment that people gain in college, there is a cost; an economic cost.  The worst day in my life was the day I graduated from undergraduate school.  I had just broken up with a long-term girlfriend, I had no job lined up, and I knew that I was never going to live within the same proximity of my fraternity buddies.  From here on out, I'd have to seek a job, manage money (I had basically no money), and worst of all, pay for the fun I had.

Student loans are a fairly recent issue.  When my dad attended college in the 70's, tuition costed less than a textbook does today.  Of course, inflation is bound to raise the cost of anything, but there is no mathematical basis to support inflation being the sole cause of the skyrocketing costs of college.

I have a huge moral issue with 2 things:  the loan companies and colleges.  Every year, colleges raise their tuition all across the nation.  It's an annual thing.  While it is true that colleges are mainly expanding, they will never be motivated to lower the cost of tuition; if the current price still attracts students, they might as well keep racking in that money.  When I began attending Heidelberg, annual tuition was $20,000.  Heidelberg.edu shows that it has since risen to $25,000  Through financial aid, the cost was roughly reduced to half of that.  This does not even include room & board, and textbooks.  Textbooks can be made cheaper by checking out the site:  www.dealoz.com.  I recommend finding your required books through that site; it will be a major financial relief to find a book slightly used.

Right before I left Heidelberg, I received a letter about from the University about how they know how bad the economy is... but they were going to raise tuition by another $2,000.  It didn't really affect me since I was on my way out.  What did affect me was the pressure from student loans.  I had to almost impulsively decide how to figure out how to pay them back.  I had 6 months before statements would start arriving.  After a month, I applied to John Carroll University for a Master's in Education and teaching license.  After acceptance, I was able to defer my current loans, but guess what?  I had to take out even more in loans.  This was a gamble.  What if I still couldn't get a job after getting my Master's?  That would be very bad.

The point that I am making is that College functions along the same paradigm as indentured servitude.  Many of us attend college to escape poverty; one of the few ways to gain skills in this economic market is to earn a college degree.  Many of us should not go to college because we do not have the needed skills to do so.  Some of us can find our skills through a trade school, such as welding or plumbing, or machinery.  Such individuals surprisingly make very good money; more than a teacher with a Master's degree.  Those who do not attend college start working, and after a few years, we start to realize that we need to make a living of our own.  Working at a gas station will not pay the bills; as our friends finish college and move on to bigger and better jobs, we are still stuck working a job we could have had at the age of 16.

Student loan companies lobbied for legislation that would allow for substantially larger interest rates on student loans.  For whatever reason, they weren't profiting enough off poor, young citizens, and they felt entitled to a larger profit.  This is why I don't believe in free-market politics; unregulated economic activity inevitably favors the more advantaged members of society.  The legislation did not pass, and for good reason.  There is no reason for college to have to cost substantially more than it once did, and student loans are only making it worse for society, for all of our young college grads will not be able to participate often in the market for several years.  Without young participants, the housing market will crash again, and other markets will fail because nobody has money to spend.

Fortunately for me, I lucked out.  My grandmother's dementia finally gave way, and she passed away in the summer, leaving a large inheritance for me to pay back all of my loans.  I got lucky.  People can spend as much as 10 years or even more trying to pay them back.  Society never used to demand such indentured servitude.  I won't tell students to not attend college, but costs can never go down unless students across the nation begin a movement refusing to attend college.

The Big Bang Theory and Stereotypes about Science People

Big Bang Theory fascinates me, because it uses creates humor out of the stereotypes that arise from the intellectual superiority of scientists.  As a person well immersed in the field of physics, I always find it difficult to understand the thoughts and behaviors of others.  I am trained to approach everything mathematically and logically, and I seldom deviate from that approach.  Many physicists function that way, and here are some interesting observations that I made from watching the show.

Sheldon Cooper:  Sheldon has Asperger's Syndrome.  Wikipedia says that the show's creators try to deny this detail, but think about it... Sheldon often only thinks about himself, and he never takes himself as a rude, condescending character; he just assumes that all people are capable of reaching the same conclusions as himself.  Sheldon lacks social skills to the extreme, yet is a well-versed dancer.  Despite being raised by a deeply religious mother, Sheldon rejects all religious indoctrination, as it is not consistent with his model of how the universe works.

Leonard Hofstadter:  Leonard is the most realistic character on this show.  He has lapses in social judgment, but he usually is aware of his own situations, ethics, social customs.  His nerdiness certainly defines important aspects of his character, but he is capable of knowing when to bring up nerdy topics and when not to... usually.  Leonard reminds me of my college adviser, Dr. Lemley.  Lemley wrote a physics test on Klingon ships moving in outer space at the speed of light; this is a clear indicator of the nerdy side to himself.  He also gets along with people, has some odd characteristics, and has a healthy, happy family.

Howard and Rajj:  I am lumping both of these characters together because I observe their struggles with women.  Most people perceive physicists to struggle with women, and most people are right.  I think the reason that this is often the case is that physicists think on a purely logical basis... all the time.  We are programmed to think this way, and when we see ourselves talking to a beautiful woman who, like most people, knows little to nothing about physics, we don't know what to say.  We do know that talking about work won't interest her, and if we are nerdy outside of work, what is there to talk about?  Star Wars?  Settlers of Catan?  Most people in general aren't interested in Settlers or Physics, so it's no surprise that it is difficult to impress a woman with such knowledge.

Penny.  Penny is not a dumb blonde.  She looks dumb because she stands near guys who know way more than most people in general.  She works as a waitress, struggles to make a living, and finds herself chatting up Leonard and Sheldon just to pass the time.  She often mediates between the audience and the characters by showing how it is unreasonable to expect ordinary people to understand Newton's laws and uncertainty principle.  I think it's kind of sad that we don't value mechanical understanding of our world a bit more.

I had a college professor who is not like any of the above.  Dr. Velasquez is a character with very good social skills; he is an international competitor of ballroom dancing and an nth degree blackbelt in three different martial arts.  Of course, he also has a PhD in (I think it is solid state) physics.  He is a great public speaker and earns much respect from the community...

The thing that interests me are the stereotypes about science people.  I have a Dilbert comic posted outside my classroom where Dilbert attends a scientist anti-defamation league meeting where they want to dispel the myth that scientists have no social lives.  Nevertheless, they agree on Saturday night for their next meeting.  Why are so many scientists characterized by a lack of social interaction?  Every field of study requires people to interact with each other, and science is no exception.  Personally, I used to shy away from many social situations because I was interested in things that I knew would bore most people.  Sometimes I'd talk about them anyway, just to show off how smart we scientists are.  Since then, I have developed some interests of "normal people," such as sports, video games, and videos of funny kittens on youtube.

I think I have explained the mechanism that feeds the stereotype.  I also think that a truly educated person can talk about anything.  Einstein had pretty good people skills; he was also a gifted musician, an artist, a literary scholar, and a social activist.  He once turned down an offer to become Israel's Prime Minister.  Dr. Velasquez is another example of a jack of all trades, as explained before.  

I strive to be the same same thing in my own life.  I have my strong set of political views.  I appreciate some works of literature; I play tennis, I used to play billiards, I was a stand-up comedian in college, and a pretty good one at that.  I once won a tournament of guitar hero, having only just started the game 2 weeks prior.  The person I beat had been playing for more than a year.  I have since dropped the game, for the real instrument.  I think the best thing a person can do in life is enrich themselves in as many things as possible.  Albert Pujols is a multi-millionaire who once his baseball career ends, despite his large financial success, he will not likely experience the pleasure of intellectual success, and success across several different subject areas.  My advice to my students is to enrich themselves and develop multiple passions.  You never know which one turns into the career.  Even then, the average human will change careers over 3 times in a life.  This means that you will probably change your major in college at least once, if not several times.  Many students of mine could major in anything they want.  This ability may seem like an ill-gotten gain, but in the future, it opens up so many possibilities.  Don't develop the attitude that any content area won't be useful in life, because the skills you gain in that class may be very important in the future.

Why I chose Physics

My senior year of High School, I took a bunch of classes that sparked the beginning of my intellectual pursuit.  I took AP Physics B in the morning, followed by AP government, then French 4, World Literature, and Calculus.  Every class I took taught me something that I still think about several years later.  Here's the breakdown:

AP Government:  I'll never forget having a government teacher who was a self declared socialist.  I learned more from him about our political system than I ever imagined.  I remember hearing about Marx's theory of political influence, and my goodness, he was right!  Marx was an arrogant, anti-Semitic aristrocrat who hypocritically believed in social egalitarianism, but his understanding and predictions of political control are astoundingly immaculate.  He predicted the rise of corporate oligarchy and the decline of the local, small business and the struggles that the working class would have to endure until they no longer could.

  I am so fortunate to have been born into a middle class, and that I was able to maintain such status.  I remember working at a Big Lot's, where much of my pride and dignity had been stripped.  I got flack from management for refusing to work on the day of a close friend's wedding; we had to attend a seminar on customer service, and the presentation may have well been geared towards 3 year-olds; I had to hear about how horrible unions are from guess who:  corporate office.  Of course corporate is going to brainwash us with this anti-union propaganda.  Worst of all, I had to take orders from people with half of the intelligence of my own students, who are teenagers still learning about the ways of life.  Needless to say, I gladly quit my job working retail for a corporation clearly bent upon subversively manipulating its subjects.

French 4:  I carried a conversation with a family from Belgium a few months ago when I went to San Francisco.  It had been over 6 years since I had to ever talk in French, and there I was, speaking it as if I never stopped.  The memories of learning French never cease to inspire me, as I feel that a well versed individual should fulfill oneself in the speaking of another language.

World Literature:  If there's anything I learned in World Literature, its that our culture is only a tiny speck on the world map.  Many western stories came from other sources that were around long ago.  I also know that whenever we do something in the United States, other countries are observing and critiquing our actions.  This is because our culture seems to be set on the idea that we are this exceptional society that can function in of itself without any regard for international appeal.  I also learned in World Literature that religion is a product of society; not the other way around.  Notice how historically, Christianity has speciated into different life forms, including several different denominations that correlate from the same principle.  We have  the Catholic church, the Protestant Church, the Methodist, Presbyterian...  The history of religion resembles that of a fossil record, showing how religions branch out rather than being independently created.

Calculus:  I enjoyed Calculus.  I didn't use it nearly as much, but it did enhance my knowledge of physics.

Physics:  Here we go.  I hated science in 10th grade.  I didn't believe that I was ever going to go into it, and had no interest in it.  This is because I took biology.  I found the study of organic compounds and cells to be somewhat boring and unappealing.  I was also a lazy kid who just wanted to blame the teacher, but that's another story.  Out of spite for my 10th grade Bio teacher (who is really a good teacher, but again, I was a lazy kid), I decided to enroll into AP chemistry my junior year, and I vowed to get an A in that class.

Not only did I get an A in AP chemistry, but I also earned a 5 on the test:  the highest possible grade on an AP test.  I loved chemistry because I was able to integrate mathematics into what I was learning.  Mathematics has always been a hobby for me; I study sabermetrics (advanced baseball player analysis) on the side as a sort of hobby, and I can't get over how useful it is to quantitatively reason in mathematics.

Senior year, my chem teacher recommended me for AP physics.  Despite my success in chemistry, I was still intimidated because I heard about how hard it is to learn...

My physics teacher in high school was the most odd teacher I ever had.  His name is Mr. Ramsey, and he still teaches physics at Mentor High School.  He has since aged, and is near retirement.  He is a master at web design, yet can only type with 1 finger.  He was absent-minded about every assignment he gave out, never made answer keys, and never solved problems in front of students.  We were so frustrated in that course, but we learned so much because we had to do it ourselves.  Most important, he had a sense of humor.  I owe a great deal of what I know and do as a physics teacher to him, because without him, I would not likely have found the inspiration to not only study physics, but teach it.

 He and I later became good friends when I decided to become a physics teacher several years later, and I came to really appreciate all he had done for me.  Last year, we both worked together in Mentor, OH, to help run the Science Olympiad team.  I found out about how attentive, caring, and aware of student situations he, like any good teacher, had to be during all these times.

I always enjoyed the problem solving aspect of physics.  I liked setting up systems of equations, finding relationships through derivatives, and best of all, being able to picture the situations.

In chemistry, you have to trust your calculations for an answer; 10^21 molecules does not tell you much if you are trying to think if your answer makes sense.  In physics, you can reason that it does not take 100 s to fall 3m, or that a car moving at 34 m/s will not reach 1,000 miles in 880 seconds.  The ability to mathematically problem solve and qualitatively evaluate an answer inspired me to pursue physics.

In college, I realized that much of modern physics is counter-intuitive.  Everything you thought you knew from learning physics in high school is kind of wrong.  It was a major blow to the brain finding that out.  It's not that I teach a dead language; it's just that these equations only work for small speeds and large objects.  Quantum physics creates all kinds of paradoxical conundrums; Einstein's relativity produces the twin paradox, where a brother can become much younger than his twin by traveling in outer space at a speed near that of light.  Another paradox is that an 8 ft pole can fit into a 6 ft barn perfectly straight, if the pole moves close to the speed of light.  In quantum physics, an object can exist in multiple universes at the same time, and that our lives might as well be virtual reality games, where we control the story.

I contemplated changing my major; I couldn't accept these seemingly contradictory realities.  I didn't know what to choose instead, so I kept on with physics.  I learned something that very few people ever try to understand.  People concede that I'm some sort of genius because I studied physics.  Looking back, I am glad that I studied the fundamental science of the physical universe, and I owe a great deal of help to my college mentor, Dr. Terry Lemley at Heidelberg University, and the head of the physics department, Steven Velasquez.  I'm no genius, but I like to think that I'm not light-years away from being one.

My appreciation and passion for physics that I demonstrate on a daily basis is not an act.  I think it is the most amazing subject in the world; explaining the most fundamental of all real world phenomena.  Physicists have, throughout history, always demonstrated a holistic balance of rational and creative muse, never shying away from thinking, problem solving, and discovering just how amazing our world is.  Not much compares to the feeling that one acquires from proving an answer that is consistent with the discoveries of others.