The Most Interesting Lecture of all Time (and Space)

What you're about to read is the Holy Grail of physics lectures.  Well... it's the introduction to the Holy Grail of physics lectures.  It's the lecture every professor wants to give and the one every student wants to hear.  In the next couple of paragraphs, I'm going to lay down the foundation of Special Relativity and explore some of the paradoxes that arise from it.  This is some seriously cool stuff.

Within this post, I'm going to include links to several helpful videos.  I'll try to write in such a way that you don't need the visual aids, but I highly recommend that you click the links as they come up-- they will prove very helpful in wrapping your head around this new way of thinking (I'm speaking from personal experience).

First thing's first.  If we want to understand special relativity, we need to understand "frame of reference,"  Simply put (as everything should be), this is just the idea that things appear to move differently from different perspectives.  For example, if you're driving your car around your neighborhood, the bobble head on your dashboard seems to sit still (aside from the occasional nod it gives you when you slow down or speed up), while the mailboxes, houses, and and old men sitting on their porches are zooming past you.  From the perspective of one of those old men, however, it's you who appear to be traveling very quickly, while his glass of lemonade sits motionless beside him.  Video.

This idea probably isn't new to you!  This thought first crossed my mind sometime around third grade, when I was tossing a tennis ball up and down in the back seat of our truck on the way to grandma's house.  How is it that our vehicle can be traveling so fast, yet the ball doesn't fly backward when I let go of it?  As you could easily reason, it's because I'm effectively throwing the ball at 60 miles per hour (or however fast the vehicle is moving) every time I let go of it.  This is why cricket players get a running start when they bowl-- the velocity of the ball when they release it is equal to the combination of the speed at which they're running and the speed at which their arm is moving when they let go of the ball.

Now you're ready for the first (and most) mind-bending idea I'm going to hit you with.

Imagine that I have a flashlight.  If I aim it straight in front of me and turn it on, the light will travel at 300,000,000 meters per second (300 million m/s).  Great.  Now, let me get a running start.  Let's say I get going at like... 7 meters per second, then turn on the flashlight.  From my perspective-- my "frame of reference," how fast does the light travel?

I know, I know, you're smart enough not to fall for the trap I set.  I just explained reference frames, and you know the from my perspective, the light is still moving at 300,000,000 meters per second.  But how fast does my mom, who's standing next to me, wondering why I'm running around the house with a flashlight, see the light moving?  Well, if I'm moving at 7 meters per second, and light travels at 300 million meters per second, then my mom should see the light moving forward with the sum of these two velocities: 300,000,007 m/s!

But she doesn't.

What my mom sees light traveling at 300,000,000 m/s-- the same speed it was traveling before I took off running.

Wait... what?  Video.

Light travels at a constant velocity, regardless of from what reference from you observe it-- inertial (moving), or otherwise.

This fact is the foundation of Special Relativity, and it is not easy to swallow, yet we know it to be true.

The fundamental implication here is the first that comes to mind-- one that you might have already considered: nothing can travel faster than the speed of light, or we're going to encounter some serious problems.  For example, If I ran at twice the speed of light and flicked on my flashlight, then the light, which doesn't change its velocity with mine, would be behind me, while I'm running forward, flashlight in-hand.  Or maybe the light just wouldn't escape at all?  Once I reach that threshold of 300 million meters per second, the light just vanishes?  Who knows.  It's spooky stuff, and it can't happen.

So with the axiom that the speed of light is constant follows the rule that nothing can travel faster than the speed of light.  Nothing

However... as things move faster and faster, approaching 300,000,000 m/s, some interesting "paradoxes" arise.  I say "paradoxes" because these aren't paradoxes at all!  They are truths that follow from that first axiom: the speed of light is constant.  We call them paradoxes because they counter the intuition that we've developed from a lifetime traveling at ordinary, "non-relativistic" (AKA not very fast) speeds.

Now, when I set out to write this post, I planned on explaining some of these paradoxes in my own words, but then I realized that if you just watch the videos that I provide links to, you'll get a better, clearer, more complete explanation than I would be able to give you in a then redundant paragraph.

So what I'm going to do instead is leave you with videos explaining the two most famous paradoxes of relativity along with brief explanations, just so you can get a taste of what they're about and decide whether you want to invest the five or ten minutes watching the coolest things you'll ever see.  Then, you can ask me any questions you have about things that don't make sense or sit well with you!

So I leave you with these links and the feeling that the rug has just been ripped out from under you because that's what learning new things about physics does each and every time.

The Twin Paradox:
This is the idea that if you start out with two people at the same age (twins), then send one of them, person A, off in a spaceship at really, really high speeds, person A will return to earth younger than person B.
[this is because of something called time dilation]

The Pole-Barn/Ladder Paradox:
In this paradox, a 6 foot pole can fit completely into a 4 foot barn.
[this is because of something called length contraction]

"All Life is Precious" -- But why?

The title of this post was taken from AMC's original series, The Walking Dead.  The show is about a zombie-infested post-apocalyptic world.  I'll avoid dropping any spoilers, don't worry, but a character in the show lives by the phrase "All life is precious."  They don't kill (I'm invoking 'they' as a gender neutral singular here-- have no illusions: no one else hesitates to pull the trigger).  

It wasn't The Walking Dead that gave birth to the content of this post, but the maxim of this character steps closely with something that I've put a lot of thought into over the past few years.  It's an age old question and a favorite topic of discussion between armchair philosophers:

What makes life valuable?

I'd be lying if I said this was the way I phrased the question a few weeks ago when I was walking by the Grim Dell on my way to dinner.  The words I originally chose were: "What makes my life valuable."  No, I'm not having an existential crisis.  I believe that God gives my life value; I am his ambassador and servant., and what purpose could be more fulfilling than serving the king and creator of the universe?  (None come to mind.)  No, I know why I value my value the breath in my lungs; I was more interested in what makes my life valuable to others.

Though I'm still being too general.  Chances are, anyone who shares my beliefs will agree that the church is the body of Christ, placed on earth to accomplish his work.  I need to narrow my search.

What makes my life valuable to non-Christians?  Now we're getting close to the question I really asked myself back on William and Mary's campus.

A few answers came to mind, though I didn't find any of them particularly satisfying.

I might be a pet-- a companion.  Many people find comfort in the company of others.  There is safety in numbers, conversation breaks the silence, and having more people around presents the opportunity to participate in a wider range of activities (it's no fun playing catch or Euchre by yourself).  Perhaps that's what makes me valuable to some of my friends: our relationship is a classic example of mutualism.  The dog gets fed and petted, the human gets a loyal and indiscriminately-loving companion.  Everyone is happy. But what if I'm not your friend?

I might be a processor.  I have spent a lot of hours learning to analyze data and go through computations.  A computer can do math problems much more quickly (and correctly) than I can, but I can feed it the relevant information or even program it to do what needs to be done.  I can read, I can write.  My hands are useful in a lab.  Maybe I'm a processor and some future employer is eager to roll up to me in his swivel chair and input commands so that I can make him more money.  Again, we would have a mutual relationship where he gets another brain to work toward some task that will make him lots of dollars, and I get a few of those crisp Washingtons for my trouble.  But what if you don't need another (weaker) computer?

I might be a tool.  Maybe what gives my life purpose is simply my ability to do work.  Because I can apply a force, I am valuable to society.  Just fuel me up with a cheeseburger or a potato and I'm ready to move some rock or hammer some nail.

Now we're getting to the bare bones of the question.  Again, the question is: What makes life valuable?

What separates the living from the non-living?  The ability to move?  To apply that force necessary to do work?  Google told me that life is "the capacity for growth, reproduction, functional activity, and continual change preceding death."  What is it about the ability to grow, function autonomously, and reproduce that equals value in life's big equation?

I'm a better pet than a rock.  I'm a better processor than a river.  I'm a better tool than a cloud.  But is my value to society as a useful object the only thing that gives my life force purpose from a non-believer's perspective?  I'm not saying it is, but I struggle to reason that it isn't.  After all, I've always said that if I wasn't a Christian, I'd be a utilitarian.

Furthermore, I'm a better pet than a plant.  A dog is a better pet than a plant!  And I'm a better processor than both a plant and a dog.  Does there exist some hierarchy of value when it comes to life?  Is it okay to kill and eat vegetables but not meat, or is it wrong to eat either?

Is all life really precious?

Now usually at this point I'd drop some opinions on you guys.  Or I would find some convenient way to redefine a key word or twist a fundamental idea of the question to make it so we could all sleep okay at night.  But I already told you my opinion: God gives me purpose and value.

To be 100% honest with you, I don't understand the idea of the inherent value of life from a non-Christian perspective.  It seems that we all grow up just to die if our purpose is tied to this world.

If I dedicate my life to better understanding the universe or inventing some convenient machine, all I've done is made it easier for the next generation to live and die more comfortably, and that's not enough for me.  I don't know how it's enough for anyone.

I Don't Talk Politics

I don't talk politics.  I don't know anything about them.  But do you find it interesting that our nation is split pretty much 50/50 on political issues?  Rather, do you find it interesting that half of our nation identifies with one party and half with another?

Now, don't get caught up in semantics here, or you'll miss the point.  I'm not saying that there are exactly the same number of Democrats as there are Republicans, nor am I saying that these are the only two political factions.  What I'm saying is that there are two main political parties and the numbers are close enough that your vote counts.

Maybe that doesn't seem strange to you, but like... shouldn't it?  Shouldn't people generally agree on this kind of thing?  Or shouldn't one argument be more persuasive than another?  On one hand, it seems odd to me that we the people would be so evenly polarized on these issues, but on the other maybe it isn't so surprising.  I will now give several reasonable theories on why this even split exists-- the last is my favorite and the inspiration for writing this post.

One.

People have different circumstances, and one's circumstances play a huge role in one's opinions about what is best for the nation.  It's undeniable that we become biased because of our situations.  When it's cold, I imagine that I would take any heat over Jack Frost's nipping at my nose, yet, when summer rolls around, I reason that if it was winter, I could just bundle up and be a much happier camper.  It's been said that the goal of education should be to become conscious of these ideologies-- maybe that's another blog post.  Back to circumstances.

I find this idea difficult to agree with.  Circumstances are almost wholly dependent on wealth.  Right?  If your income is six digits, your house is probably bigger, your food is probably tastier, your clothes are probably nicer.  People say money can't but happiness, but no one actually believes that.  Now, we've all seen those graphs of "how many people hold what percentage of the nation's wealth," and from this illustration we can see that it's not a 50/50 split.  Few have very much.  Many have very little.  So if one's circumstances dictate one's voting habits and one's income dictates one's circumstances, then it doesn't make much sense to say that this is a reasonable explanation for the split.  That being said, there are factors other than the cash in your pocket that determine your quality of life, but we don't have time to explore every lurking variable, so we'll continue.

Two.

People have different ideologies.  I mentioned ideologies before.  If you're not voting on the basis of "what is best for the country" maybe you're voting on "who agrees most with my beliefs."  Maybe political issues equate to moral issues for some.  I mean, if a candidate for president thought that murder should be legal, would you vote for them?  Again, that's another blog post, but you understand what I'm trying to say: people don't vote based on what is objectively best for the nation, they vote based on what is most important to them.

This argument really isn't reasonable.  To say that this accounts for the even divide of our nation makes too many assumptions.  First, that most people vote based solely on ideology-- this likely isn't the case.  Second, that people are split evenly on a moral framework-- this seems counter-intuitive.  Third, that people with one belief will share a slew of others-- this makes sense for a religious nation which would be bound to some standardized moral code, but it is no longer popular (or accurate) to say that we are a particularly religious nation.

Three,

If you have a bag that contains 5 red marbles and 5 blue marbles, what are the odds that you will pick out a red marble if you randomly take 1 out?  This calculation is trivial.  There's a 50% chance.  What if it's random?

You're already mentally objecting.  Naturally.  People take pride in their team.  You like the Democrats because you believe in what they stand for!  Right?  You're a Republican because big government sucks!  Yeah?

I already told you I'm politically ignorant.  I will not engage in political debates over this post, but it seems to me that there are truths on both sides of this coin, and many people have just flipped it.

PS:  I didn't revise/edit this.  It wasn't worth it.  Thanks for not holding it against me.

Einstein, Bears, and Mental Health at William and Mary

Sit Einstein (not actual Einstein-- just the proverbial smart person) down in a room with a problem he or she couldn't hope to solve (we know they exist).  Never expose this person to anyone except the people overseeing the experiment, all of whom pretend as though they know the solution to the given problem and act as though it is simple.  Now, our proverbial smart person feels more like a proverbial dumb person.

Obviously, right?  Intelligence is relative.  I really haven't said anything profound, and, as is the case with most of my blog posts, I probably won't, but this is interesting, right?  Our Einstein doesn't even have to be the dumbest person in the room to feel like the dumbest person on earth-- as long as the only people he comes into contact with put on a convincing enough air of superior intelligence.

I feel like this happens all the time in the media, in conversation-- really in any mode of self-expression you could imagine.

I'm not going to give the speech about the digital age and being more concerned with our image than our actions.  I won't make the claim that we found our self-esteem on likes and shares.  Honestly, I'm kind of tired of that story, and I feel like it's age-old.  Haven't we been concerned with symbols of status for all of recorded history?  Like, I'm a complete idiot when it comes to stuff that happened a long time ago, but I'm pretty sure kings wore crowns and rich people wore purple.  The whole idea of compensating for insecurities by trying to paint a more perfect image of ourselves is nothing unique to the twenty-first century.

This is a bit of an aside, but if you're reading it, then it probably comes full circle in good time.  I think it's interesting to look at the way this makes other people feel.  Right?  Like, I've posted several pictures of my physics homework on social media in the past.  The average bear can't make heads or tails of it (half the time, neither can I).  It looks complicated and foreign.  This probably affects said bear in some way!  The bear probably doesn't like looking at what his fellow forest-beasts are doing and thinking "Hmm.  Well, I have no idea what that means."  Do I think about that when I hit post?  Hopefully not.  You'll have to take my word that I don't.  But I when I see Suzy's Computer Science test or Jimmy's Arabic homework, it opens my eyes to the things I don't know.  When I listen to sports analysts, I have no idea what they're talking about-- I don't speak their vernacular.

So now we get to be psychologists.  How does that make us feel?  It's a good question, and I think everyone has a different answer.  I don't feel dumb when I see everything Suzy and Jimmy know that I don't.  But I do feel kind of small.  I know a lot about some things.  Physics.  Math.  A few video games.  Euchre.  But I know very little of most others.  Language.  Culture.  History.  Now, I said I don't feel dumb when I see what other people know about the things I don't have much experience with, but what about our Einstein?  Let's say math is his thing, and the problem his overseers give him is to discover the lost proof of Fermat's Last Theorem.  No one has done this, yet, but they're pretending this problem is elementary (Watson)!  Poor Einstein would feel destroyed by this, wouldn't he?  Yet I'm not destroyed by the fact that my friend Jacob knows a lot more about history than I do.  I guess the difference is context.  Our experiment kind of assumes some level of naivete, limited exposure, etc...  We're all pretty well aware that we're not the dumbest person in the world, right?  Now we're getting to the point.  You feel it, don't you.

Our final stop on this intellectual journey brings us to academia.  I rarely post a Facebook status saying "I got a 54 on my Classical Mechanics exam!"  That's not really a thing.  But I might post that "I had a rough semester in Class Mech II, but I managed to pull out an A in the course!  Praise God!"  Why post one and not the other?  Obviously, the first makes me look like an idiot and the second makes me look like a hard-working, successful student who doesn't crumble in the face of hardship. I don't need to belabor that point-- you get why we publish what we do.  But what does this do to others?  Let's go back to our bear!  Let's say some other furry beast didn't end up with an A in Class Mech.  They see that I did and now they feel belittled.  In fact, anyone who posted much of anything about their grades probably talked about their good ones.  Now the sad bear is practically in Einstein's position because everyone is pretending like they know the proof to the Fermat problem.  Little does the grizzly know, I got a C+ to his or her A- in Electronics or a B- to his or her B+ in Quantum.

I feel as though this is the biggest issue at William and Mary.  I love my college.  Ask me one day to tell you about all of the good things.  But one thing we do poorly is portraying ourselves in a realistic light.  Here comes my psychoanalysis-- ready?  We all came from the top 10% of some high school somewhere.  We had good grades.  We had good SAT scores.  We were big fishes relative to our tiny ponds.  All of a sudden, someone drops us in the ocean, and we realize that we're not as big as we thought we were.  We question whether we can even survive in salt water.  We struggle to beat the average.  It's a shock!  It is!  It's scary.  It's unnerving.  Many of us went from success without effort to failure with blood, sweat, and tears in just one year.  So how do we compensate?  We tell all of our friends how much work we have to do and how hard our tests are, omitting the lazy Saturdays we've spent watching Netflix, then we post to Facebook about our amazing grades, neglecting to mention our failures.  The result?  Everyone feels like they're drowning.  If we were just honest with each other about success and failure alike, if we were just truthful about how many hours we actually spend studying versus wasting daylight, if we were just realistic in the way we portrayed ourselves, I believe it would do wonders for the mental health of this campus-- and I have a feeling that William and Mary is just a microcosm of the world at large.

Surround Einstein with enough convincing actors, and he might just lose hope before he ever has the chance to achieve something great.

"The Best Summer of Your Life"

     On May 24, 2015, I received an email from Liz Holohan that began: "June 14th is getting closer! Only a few more weeks till the best summer of your life."  Following this statement was about what you would expect from an email detailing what you should and shouldn't bring to UVA when packing for your seven week experience as a counselor at the Summer Enrichment Program.  But that statement was so bold!  "The best summer of your life."  Really?

But believe me when I say that it was.

     I love working with kids.  I truly do.  Kids of all ages.  I've been involved with nursery, Vacation Bible School, Mathnasium, you name it.  I love kids, and for good reason!  I love their energy.  Even when it's 5:00 AM and they've been up since 7:00 the morning before, they'll still be dancing around the hall singing all of their favorite songs from High School Musical.  I love their honesty.  When they don't want to go to the pool and claim that they would rather "just read a book instead," they'll pack one instead of a towel and spend three hours of the most beautiful day of the year turning pages under a tree while all of their friends are splashing around in the water.  I love their thoughtfulness.  When dinner is almost over, and they stand up to get dessert, they'll often ask you if you want anything while they're up.  I love their spontaneity.  When they're quietly reading a book about the Periodic Table, they'll decide after a page on Sodium that it's the perfect time to claim that they can do The Shuffle and insist on standing up and proving it, even though you never said they couldn't.  I love their loyalty.  Even after you've taken away 20 minutes of their favorite part of the day and, as punishment for some form of inappropriate behavior, forced them to do a "blob of paint" puzzle that's all one color and has no corners, they'll still wish you a good night before bed and tell you jokes over breakfast the next morning.  I love everything about kids, and if I tried to list all of my favorite things I would never get to the rest of this post, so forgive me for cutting this short, but there's just too much more to say.

     Okay, you get it.  I love kids.  Now I should explain to you a bit about what I did with them this summer.  The Summer Enrichment Program (SEP) at the University of Virginia is a program for gifted high school and middle school kids.  They have to go through a rigorous application process in order to attend the camp, and all of the applicants are the naturally curious, academic type to begin with, so the campers who end up attending truly are the best of the best as far as middle and high school scholars go.  My job was to be the counselor of eight rising Freshman.  What does it mean to be their counselor?  That's a huge question, but I'll explain it to you the same way I explained it to them.  I have two jobs as a counselor: to keep my campers safe and to help them have a good time.  Keeping them safe means that I maintain an environment that is saturated with kindness and respect and void of both physical and emotional danger.  Helping them have a good time means being relate-able, building relationships with them, and leading by example and having a good time myself.  Over the summer, I saw 312 high school campers and was responsible for 24 of my own (there were three sessions, and each two-week session I had eight out of 104 of the high school campers in my suite).

     As far as writing this post goes, I'm brought to the most difficult part.  I could not decide how I wanted to try and capture my SEP experience.  Through narrative?  I have plenty of stories to tell, but I can't use names or pictures of campers, and I don't want to ruin surprises for potential future campers who might stumble across this as their sibling or friend is reading it.  Through summary?  Every session was too different-- there were common themes, but it would not do each justice to try and lump them all together.  No, I can't narrate and I can't summarize.  Instead, I'm going to do it like I would if I was still back at SEP.  Every session, in the high school camp, we have what's called a "Junior Farewell" on the last day.  Junior year is the last year that you can attend SEP, so at the end of each session, we give our Juniors the opportunity to tell all of their fellow campers and counselors what SEP has meant to them.  I'm the type to choke up, stumble over my words, and flounder in those kinds of situations, so I would have prepared a written statement (and I still would have read it through tears, as any camper reading this knows).

This would be my speech at a Junior Farewell.

     SEP.  Summer Enrichment Program.  "You're not wrong."  It's a program that happens in the summer, and I definitely feel enriched.  I definitely feel enriched.
     To enrich.  "To enhance the quality of."  To say that I am enriched is to say that I am better because of SEP.  But that's so vague. "Because of SEP."  What is SEP?  Who is SEP?  "Better."  Better how?
     From a counselor's perspective, SEP has nothing to do with classes and very little to do with any sort of activity.  Most of those things are, as each counselor has thought to themselves countless times, "for the kids." Yes, we walked you to your classes, but, for me, that was more about the chance to get to know you better and make sure that you got there safely than about the class itself.  And yes, we organized and participated in activities and had a lot of fun doing it, but my favorite part of the Counselor Dating Game and the Fashion Show was seeing the smiles on all of the campers' faces, not hearing about Pam's and Sam's sandbox or watching the baby Corticorn be born into this world.  To a counselor, or at least to this counselor, SEP is not about classes or activities, and I understand that many campers share this sentiment.  To me, SEP is about family.
     I would often greet both campers and counselors alike with: "hey, fam."  Why do you think that was?  "Fam" isn't just something that's convenient and fun to say.  It has meaning.  Obviously, it's short for family, and I meant it that way.  Some kids thought of their suite-mates as their brothers or sisters.  A few campers told me that they viewed their counselor as "the older sibling that gets left in charge, except more fun."  I know that several counselors thought of their campers as their kids.  I heard one counselor describe his job as "being a single father of eight," and multiple kids told me this summer that I "would make a great dad."  I think it's no coincidence that this theme of family came up so often this summer.  It's difficult to nail down exactly what part of the SEP family each member of the camp represents, but I think that most who were a part of the Summer Enrichment Program experience would agree that, in some way, we all grew to be one giant family.
     That's cute.  Really, it is.  It's a little cliche, but it's cute.  But how does that enrich someone?  A family isn't inherently enriching, but this one definitely had a positive influence on me.
I learned a lot about myself-- my strengths, my weaknesses.  I learned a lot about others-- their diversity, their complexity.  I learned a lot about responsibility-- the pressures, the rewards.  I feel as though these aren't things that I need to explore in great, long-winded detail.  Suffice to say these things.  A strength is that I have almost endless amounts of patience, but a weakness is that my passion for any given thing is very largely dependent on the passion of others; I could be more self-sustaining in that way.  Everyone is different, but they are equally complex and valuable.  The situations that are the most trying yield the greatest sense of satisfaction.  These three lessons have been very valuable to me, and I am better for them.
     I am walking away from this summer with countless amazing memories.  I will forever think back on the events that took place at SEP and smile.  To list a few that stand out, I will never forget my first paper plate award.  I will never forget about the two campers who sang "It's Raining Men" at Karaoke and absolutely killed it, even though I warned them that it might be difficult if they don't already know the song.  I will never forget the Junior who told me that he was up late just thinking about how he could apply everything he learned in my special topic to different aspects of his life.  I will never forget the twin who told me through tears at the Junior Farewell that I was her counselor crush, "not in a weird way, but because I just really think you're a great person."  I will never forget the times that one camper in particular smiled, even though she was always trying her hardest not to.  I will never forget the camper who rarely spoke, but who, when she opened her mouth to sing, got the entire camp on their feet in admiration and amazement.  I will never forget the secret handshakes that I had with campers.  I will never forget when one of my campers came up to me on five separate occasions within the same fifteen minute span to say goodbye after the Junior Farewell.  I'll never forget when a camper finally agreed to wear the matching outfit for our suite's performance of "Man in the Mirror," and how he ended up on his knees, singing into the microphone at the top of his lungs.  I will never forget the name of the camper that I forgot four times on the first two days (PS: I'm still sorry).  I will never forget answering questions, telling stories, dancing, or singing with the squam.  I will never forget the friendship bracelets and paper flowers that campers made me or the letters they wrote me.  I will never forget the conversations I had at social time and at the pool with campers who were gracious enough to spend that time talking to me.  There's a lot that I won't forget, and these few only begin to scratch the surface; I could write a book of all of the amazing things that I'll have the pleasure of remembering.
     Whew.  That was a lot to take in.  So I've been enriched with life lessons, I've been enriched with memories.  But there's one more way I've been enriched, and it's so obvious that I don't really even need to say it, but the way these things go is that I tell you it's "so obvious that I don't really even need to say it," and then I tell you anyway.  It's people.
     The people that I have met at SEP have truly changed my life.  I am a human of very few friends.  I will always prefer one or two very close relationships to many very shallow ones; however, the unique experience of connecting with hundreds of different people over such a short amount of time at such a deep level has left me a different human being than I was before.  I didn't just get to meet campers and counselors; we lived in the same building, we ate in the same dining halls, we did everything together.  I talked for hours with campers and counselors alike and forged relationships that will not end with my employment.  Thank you to every camper who took time out of your two short weeks to spend it with me.  Thank you to every counselor who put up with my antics and didn't ostracize me for not participating in every weekend activity.  Thank you to every member of the staff who doesn't get as much attention as the counselors for your invaluable work this summer.  I am not the person I was seven weeks ago; my quality has been enhanced-- I have been enriched.

Thank you, SEP.




**As always, please tell me if you find any spelling/formatting/whatever mistakes, so I can fix them!

God's Glory as a Function of Everything

What is the meaning of life?  Any Bible-believing Christian would say: "To bring God the most glory."  Okay.  Great.  The meaning of life, our purpose in this universe, the reason everything happens the way it does, is to bring the most glory possible to the God who created us.  I like that, I really do.  It makes sense, it provides a convenient and satisfying explanation to why confusing things happen, it establishes a greater good.  Perfect.

Now.  The most glory.  What does that mean?  Rather, what does that imply?  It's a truly profound question!  Including the word "most" implies a comparison.  This brings God this much glory, whereas that brings God that much glory, and this much is greater than that much.  It implies that glory is quantifiable-- if it wasn't, there would be no this much and that much, there would be no most.  But there is.  Therefore, if we accept that we exist to maximize glory, then we must accept that glory is some value that can be changed, increased or decreased-- it's a variable.  It's a variable in a function that takes into account everything that has happened, is happening, and will happen.  God's glory can be expressed as a function of everything.  Of course, we couldn't hope to solve this equation, but I deal with all kinds of functions that I can't solve.  It's not really about the solution-- we leave that to the computers.  It's about what the function says about the system it describes.

Okay.  Let's break this down.  We have an expression.  Our expression is "God's glory as a function of everything."  What are we trying to do?  We're trying to find a maximum.  This is no surprise!  Mathy people do this all the time.  I can't remember the last time I looked for anything other than a minimum or a maximum in an interesting equation.  This is because extrema imply a state of equilibrium, a static point where the function is happy.  I hope you're tracking.

How do we find a maximum?  We look at the rate of change (the derivative for you math nerds), and when that rate of change is zero, the function is at an extrema.  With some more mathematical voodoo, we can determine whether it's a minimum or a maximum, but I won't bore you with those details.  The point is that it's possible!

So where are we now?  The purpose of our existence is to bring God the most glory.  Glory is quantifiable.  God's glory can be expressed as a function of everything.  We can find the maximum of this function.  Good.  But what does this maximum represent?  It shows the discrete values of our independent variables at which our dependent variable, God's glory, reaches its greatest value.  In English, it describes a reality, a past, a present, and a future, in which God receives the most glory possible.  Now things are getting interesting.

What happens if we have multiple absolute maxima?  From a mathematical perspective, this means that there exist multiple values for our independent variables for which God's glory will be maximized.  That's straightforward enough, but what is our physical interpretation of this?  There can be multiple realities in which God receives a maximum amount of glory.  This might not seem that interesting at first, but this idea could go in two directions from here.  Theologically, it could be an exploration of free will manifested in mathematics.  Physically, it could be an explanation of the Multiverse Theory from a religious perspective.  We'll glance at both.

Free will.  Age old.  Often debated.  Never resolved.  My belief is that absolute sovereignty cannot coexist peacefully with free will the way most people define it.  However, the question of sovereignty aside, this whole maximization thing is a pretty elegant solution to a few of the other issues people have with free will.  How can God receive the most glory if we have any control over our destiny?  Wouldn't one shift in the independent variables cause a deviation from the maximum we talked about?  Well, anyone who has worked with differential equations knows that small perturbations about the extrema won't necessarily cause a shift from equilibrium, but the conclusion that we can draw from our exploration is that even a large deviation can drop us off at another absolute maximum, assuming the existence of multiple global extrema.  Long story short, if multiple absolute maxima exist in the function for God's glory, then it's possible that we could still bring God the most glory even with the flexibility to make our own decisions.

The second path relates to the theory of multiple universes, the Multiverse Theory.  Honestly, it doesn't quite fit, but perhaps many realities exist, each of which plays out to God's ultimate, maximum glory, and rather than making choices, all possible permutations of our decisions are played out on different stages.  I'm no supporter of the idea that multiple realities exist, and I'm pretty sure that the Multiverse Theory describes a system where all of the different universes have different physical laws.  It's the Multiverse Theory, after all, not the Parallel Universe Theory.  But it's still interesting to think about the theory as an explanation for multiple possible maxima of the function I described earlier.

Whew!  So a brief summary.  God's glory can be expressed as a function of everything, and reality is described by that function at its maximum.  This gets more complicated when multiple absolute maxima exist, but the implications of this complication provide some pretty convenient parallels to existing theories of both religion and physics.

And then I found five dollars.

A Break Through

            In order to discover something truly new, one of your fundamental assumptions has to change.

            This is an idea that I stole from a Ted Talk.  I mean, I kind of stole it from a Ted Talk.  It's not uncommon knowledge, but its implications are pretty profound.  This idea represents a barrier: the barrier between what you know and what you don't.  As a student, this is a barrier which I encounter often.  In fact, I claim that my full time job is to take a hammer to this barrier every day of the week.  However, students aren't the only people who run into this wall.  Have you ever put together a puzzle?  There comes a time in the piecing together of any puzzle when you feel like you've been given a bad box-- the puzzle-maker is out to get you, so he gave you a thousand ridiculously similar pieces that just don't fit together the way they should.  In the end, you're almost always wrong, and the feelings of frustration, hopelessness, and betrayal (because the puzzle-maker was supposed to be on your side) that you encountered at your lowest moment now contribute to the sense of accomplishment you feel when you've put together the picture that probably shouldn't have been broken up into a thousand tiny pieces to begin with.  That's what I want to talk about-- the dichotomy between despair and excitement and the way the former magnifies the latter once the barrier has been overcome.

             A topic of conversation that often comes up when I'm talking with my fellow science or math majors is the luxury which other students take for granted that is not needing to find a specific answer all the time.  Writing papers sucks.  It does.  But when I sit down with a blank Word Document in front of me, at least I know that in six hours I'll have about ten, sparkling pages that I can fork over to my professor, even if it's the worst paper I've ever written.  With science and math, you don't have that assurance.  There was an evening when Jacob and I sat down and spent hours struggling with a problem to which we never found the answer.  I filled three pages with algebraic manipulations for that one question, but eventually, we just had to move on.  There's something horribly depressing about sinking hours of time and energy into a problem which you never solve.  But I can guarantee that there was a physics student, we'll call him Jimjam Flimflam, sitting somewhere on the campus of William and Mary that same night who, after pulling out the majority of his hair while his roommate slept soundly in his warm, comfortable bed, landed on a solution that made sense-- and I'm sure it was glorious.  I bet Jimjam Flimflam gently set his books aside, stood up from his chair, ripped off his shirt, and quietly danced around the room punching the air and yelling silently in celebration, careful not to wake his snoring roommate.

            Do you know why he solved the problem and Jacob and I didn't?  He found a crack in the barrier, and he exploited it, smacking it with his hammer as it spider-webbed across the whole surface, until finally, he broke through.  That crack is the knowledge you have.  That hammer is your textbook and your notes.  And the other side of that barrier is a deeper level of understanding.  The thicker the wall, the greater your frustration, but the greater your frustration, the more magnificent your victory.  Some people go out and look for the thickest barrier they can find and start chipping away at it.  Some people start chiseling away without realizing just how deep they'll have to go.  Some people turn around at the first obstacle they encounter.  It's my job as a student and as a scientist to learn to see the barrier as a chance to accomplish something.  It's my job to embrace the challenge of a problem that I haven't solved.  One day, it will be my job to embrace the challenge of a problem that no one has solved. 

            However, embracing the challenge does not mean overcoming the obstacle.  There are humans who have spent their entire existence on problems that they never see solved, just like there are students who spend their entire evening on problems that they never see solved.  But that's okay.  There can be joy in the struggle.  I've never won a race, but I loved running track.  I've never finished writing a book, but I've had a great time writing chapter one.  I've never beaten Arjun in Melee, but I enjoy playing him.  You get the idea.

            Here's my advice to you: learn to appreciate the puzzle.  Have fun taking every likely candidate for the gap in your sky and twisting it every way possible before putting it back on the table.  Smile at the ridiculousness of the notion that the puzzle-maker is pitting himself against you (but don't completely discount the idea).  Laugh at the simplicity of the solution when you find it.  Breaking down the barrier isn't about scribbling down the correct numbers on the page-- it's about the understanding you gained from finding them, and that's something you can't get from an answer key.