Crying About Mathematics

I recently saw this image posted on Facebook and then looked at the last 3 posts from Grammarly, the original poster.  We have a think piece on whether universities should require writing proficiency for graduation, a joke about precision and exactitude in grammar standards leading to vandalism (with indications that that's at least understandable) and a prettied up quote from John Dewey that, "Education is not the preparation for life; it is life itself."  That last one is particularly interesting in contrast with this image and it leads to the obvious implication that what they really mean is, "Education (in the arts, humanities, and soft sciences) is deeply fulfilling and enriches life to the point of making it worth living, but of course we know technical sciences and mathematics are just painful things to be suffered through."

This is probably a good example of why US culture is so innumerate (the numerical equivalent to illiterate, a term coined by John Allen Paulos) and inept at scientific thought.  This is where we get the reflex of credibility toward the phrases "experts say" or "studies show" or the news stories that butcher or manipulate statistics to serve whatever purpose hits the emotional agenda of the story.  I'll be the first to admit (and then probably go on a tirade about the problem for however long you listen plus ten minutes) that our mathematics education is just heinous and obsolete to a point that would be absurd if it weren't so damaging and dangerous.  With that said the solution is certainly not to perpetuate the idea that these things are hard, stressful, and just generally unpleasant.

I've written here before about the nobility and importance of mathematics, and this one won't be the last time I do, so perhaps I'm just belaboring an idea, but I'm going to list out some of mathematics' virtues anyway.

• Math is Mind Expanding: Mathematics deals with concepts that can go beyond normal human experience.  How often do you work with the infinite?  Did you know there were several different sizes of infinity, and that some infinities are larger than others?  I had a very serious discussion with some family and friends recently about dimensional figures and the nature of God.  I wear a metal Möbius band (a strip that has only one side, yes really) on a necklace that was given to me by my wife.
• Math is Humbling: The humanities are important largely because they teach us to think emotionally, form opinions, and understand the human experience.  Math, and the sciences (though perhaps to a lesser degree), teach us to think rationally, examine our ideas, and understand the world around us and, yes, the human experience as well.  In mathematics one thing must strictly follow from the last and we must learn to abide by the rules of the operations we're performing.  We can form and idea or an opinion just as easily as we can in any humanities class, but then we're told to really look at that, to see if it makes sense in context, and it can become starkly clear when it's not.  Humanities often remind us that how we perceive and judge the world around us matters.  Mathematics, and the sciences, remind us that the laws of systems (like the universe) don't just bend to our will because we think we have a better idea of how things should be.
• Math Teaches Self Awareness: Like my last point, the requirements within mathematics that we "stay within the lines" as we progress form one thought to the next in our process of proving, computing, or deriving new information means we need to learn to watch our thoughts, and see where they fail to stay consistent with our principles.  Learning how we think, how one thought in the mind springs from the last and whether that process is working properly or in need of reform is pretty clearly an invaluable skill that will better society if widespread.

So if math is so wonderful, why is it so often denigrated, like in the image above depicting it as something that is sure to spawn sadness and strife sufficient to stimulate sobbing?  Why is this far from the first post to the effect of, "Ooh math really sucks, don't you all agree?" that has gotten shared around?  Why do people flaunt their ignorance or lack of active engagement in mathematics with phrases like, "I totally forgot how any of that stuff works, but hey I'm never going to use it again, right?"  Why does that receive knowing chuckles and appreciative nods instead of the derision or contemplative sadness such ignorance or loss of talent should garner ("I can't remember a thing about the Civil War, but who cares?  I'm not becoming a historian," "I used to be able to play the oboe, but now I can hardly even remember the basic fingerings," "Why did I even do all of that reading in high school?  I never ended up being in a Shakespeare play or even going to one.")?

Well, there are systematic problems.  Like I said we teach math horribly (in the US at least), especially at the elementary level which means that when children are forming their emotional understandings they learn early that math is something hard and to be feared.  It doesn't help that so many who shape the culture are also the worst at mathematics and mathematical thinking.  Still, none of these jabs at "that painful and useless old field, math" seem to present solutions or even raise awareness about the problems of media misrepresentation or the need for educational STEM reform.

I've been told that it's about thinking differently, that the jokes are just trying to say, "Oh man, my brain sure doesn't work that way," but mathematicians and scientists aren't sharing Facebook memes about how useless writing and art are.  The most I've seen are more along the lines of, "Boy it's really frustrating how misrepresented we are and how poorly understood and distorted our work is when presented for public consumption."  Also, I don't really buy that our thinking is all that different.  When I tutored mathematics the problem really seemed to be more about attitude.  People didn't put effort into learning or doing mathematics because they thought it was hard, boring, or just not important to them.  With effort they picked up the concepts just fine, but the attitudes that surround math made them reticent in putting forth that effort.

Math students have often been taught in what one teacher of mine referred to as the GMTED or the "Give Me The Equation, D***it!" mindset.  Try to discuss the concepts behind the figures, the real meaning of the numbers and symbols and they shut down and demand you give them a simple formula so they can mechanically plug numbers in.  Math education is too often a "human programming" job, using drills, memorization, and routines to create humans that will carry out operations to compute a value.  This must change, but can't if people believe that actually thinking about math is something they're incapable of because, "their brain just doesn't work that way."

So I beg of you, respect mathematics.  Let's leave behind the antiquated views of math as prima facie unappealing as we leave behind the systems that have made thousands fail to understand the beauty and wisdom it contains.  Let's elevate our understanding of ourselves by doing meditative mathematics.  Let's elevate our understanding of the universe by understanding the language in which God wrote it.  Let's create a society that values this great field of human thought and endeavor that's gifted us the computer, engineering, and so much more.  Let's create an intellectualism that, to paraphrase the apocryphal inscription above Plato's Academy, lets none but mathematicians enter; not out of elitism or to exclude readers, writers, artists, and other so-called non-math people but in recognition that a complete philosopher will be mathematician in addition to artist, reader, theologian, writer, and more as he or she embraces all the many worthy areas of endeavor in the vast yet limited expanse of human knowledge.

Your Moral Earth's Magnetic Field

I've heard people talk about how important their moral compass is to them.  What this means can be something different to any different person, but one definition that I think matches most people's conception is, "a natural feeling that makes people know what is right and wrong and how they should behave."  Are the natural feelings we have really what should make us know what's right and wrong?

Doing what's natural may not be a terrible basis for morality, but it's not a good one either.  We have a number of pack animal and cooperative instincts that guide us toward some caring and concern for our fellow man (and remember man is gender neutral in this context).  These also create an aversion toward malice in many contexts, which is also good.  Our instincts don't stop with these, 'love your neighbor' drives though.

Being a pack animal leads to a set of instincts, and while some of those are positive like what's stated above others are decidedly negative.  It leads to a tribalism, probably due to competition with other packs.  We protect our own, but those who aren't are own are usually fair targets for whatever we can dish out.  This is why looking at history we only seem to have been fighting against racism, sexism, or similar discrimination for about a century or two, and to some even that's being quite generous.  There's also significant drives to personal status and individual gain.  We want the pack to be strong, but we also want to be the head of the pack (or at least be very secure about our position in it) and there's a good chance we're willing to trade the good of our group for a high position in it, too.  This is why children throw tantrums, politicians and important businessman are as willing to admit mistakes as they are to part with teeth, and people gossip about the shortcomings of acquaintances.

This leads me back to the idea of a moral compass.  Truthfully, I think it's a good analogy as long as we remember one thing: a compass doesn't operate in a vacuum.  A compass is a magnetized needle set on a spindle (or sometimes in other ways, such as suspended in a liquid).  It points to the north because it aligns itself with the Earth's magnetic field.  In morality, this leads to the question that might be much more important than how is your moral compass, but what is your moral Earth's magnetic field.

What things external to ourselves help us understand what is moral and what is not?  Is it divine scripture?  Public opinion and associated feelings of dignity or shame?  Articulate and interesting discussions on ethics?  All of these have flaws which must be examined and guarded against and all have certain merits as well.  Compasses can be disrupted by anything that produces strong magnetic fields, like high electrical current.  Precise navigation may also require an adjustment between magnetic north and 'true north' since the Earth's magnetic poles aren't perfectly aligned with her north and south poles.  Just like a compass will not point true in a lightning storm or around power lines we should learn where our moral compass may fail to point us true and why if we want to stay true to our moral north wherever we go.

A Personal Oddity of Emotional Expression

I'm a scientist.  I'm not a poet, an artist, writer, or orator.  Well, I think there's a pretty convincing case to be made that mathematics and seeing the beauty of nature in the laws that govern it have artistic merit, I'm at least an amateur writer (I have, like I suspect many do, a few beginnings to books, short stories, or articles), and am actually a pretty decent public speaker (though maybe not anymore, I haven't really done any public speaking for quite a while), but I'm speaking here to my outlook on the world and my communication with others and a scientific outlook has strongly influenced these aspects of who I am.  There's two things that I find especially influenced by this background; objectivity and concern for clarity.

I explain that so I can explain this, it's very difficult and a little odd for me to tell my wife I love her.  Not because I don't, I'm madly in love with her.  Not because I think there's anything wrong or strange about it either, but because it's so hard to know what I'm saying.  Often when we are sitting in our apartment together I let those words, "I love you," sum things up, hoping that my feelings are transmitted correctly.  In other moments though, when I want to expound on what that means, on the way I'm excited by her beautiful form, the softening spark in me of her amazing smile, the joy I take in her fun personality, or the deep passion when I notice how well read and thoughtful she is, I don't know what to say.

One thing is I feel like I've said it all before, and I hate repetition.  Rather, perhaps, I know that expressing something in a new way is more powerful than repeating something you've heard before.  Heard enough times anything can seem clichéd.  How many different ways are there to say, "You're beautiful and I'm very attracted to you," though?  I have a fairly formidable vocabulary, but still there are only so many synonyms for beautiful, happy, and love that one can use meaningfully.

Often, and bear with me through the cheesiness of this statement, words seem inadequate.  I can tell how I'm feeling, but how do I express that?  And moreover, when I feel something so powerfully, how do I express that with equal power?  If I'm to be clear in communicating my feelings, what do I do when I feel something which seems more potent than the words I've been using.  Moments where recognition of all her glorious beauty flares up in a way that I guess I've felt before, but certainly feels new and exhilarating surely can't be expressed in a simple, "You're so pretty/beautiful/stunning/gorgeous/sexy," when I've already said that many times before, ¿can they?

I've mentioned before that I have a certain emotional austerity.  That doesn't mean I don't feel strongly, I do. It does mean I usually hold off on expressing what I feel, and moreover that when I do I try to strengthen what I say about those feelings in an alloy of emotion, thought, reason, possibly evidence, and probably sources.  I can't really do that when I express my love for my wife.  I know it's my subjective experience, I know that it's the way I feel, heck I even have an idea of some of the neurochemistry and cerebral circuitry that's powering and processing it, but still my love is real, and I want to let her know that.  I'm learning a lot as I learn how to say it.

Love Day By Day

My fiancée and I met with a friend of mine recently and in retelling how we met it was noted that the story wasn't, "love at first sight."  As deeply in love with my bride to be as I am it did cause me to wonder a bit.  I do think there was some initial attraction between us way back then, but ultimately I agree there was no falling in love head over heels upon laying eyes one on the other.  As I look back on our relationship it's grown over time, slowly and gradually.  We don't have love at first sight, but we have what I'm calling love day by day.

Love day by day is that understated love that's expressed between two folks consistently and sincerely.  It's us saying our daily "I love you"s and wanting to spend time with each other.  It's trying to find ways to make the other person happy.  I could go on, but don't wish to belabor readers with a sappy list.  Going back and reading over this I'm almost getting a little snide myself.

I would like to discuss the triangular theory of love, though.  It floats around in relationship advice, therapy, and books and promotes the idea of love primarly being made up of intimacy, passion, and commitment. Intimacy and commitment without passion is friendship, and other combinations can define other relationships.  I'm prone to a certain measure of emotional austerity and suspect it would be difficult for me to ever feel "love at first sight", but from the descriptions I believe it to be a magnificent burst of passion toward another.  A couple can feel this and then grow in intimacy and commitment to match the passion they feel, and I hope those who live giving their feelings greater quarter than I do do so.

That said, love day by day is based around commitment.  It's commitment that comes easily because we feel intimate and passionate about one another.  Commitment is a powerful concept, and - likely due to the aforementioned emotional austerity - I feel more important for a relationship than passion.  Being dedicated to another is what will allow one to break down their barriers and their pride and allow themselves to be vulnerable in the unnerving depths of intimacy.  I've always belived passion and physical affection in particular should represent a deeper commitment, and as such I've become more passionate toward my fiancée as I've committed more and more to her.  Commitment lasts beyond hurt feeling and dull days, and I'll gladly live without love at first sight, as long as I have love day by day.

Mathematics is a Godly pursuit

I had this thought after tutoring one day and I've been meaning to write on it for a while.  Many friends and family of mine will be familiar with my love for mathematics and my feelings of anathema toward the apparently acceptable innumeracy of current American culture at large.  While there are numerous arguments on the basis of how useful mathematics is, what a powerful tool it is and how important it is to understand statistics (such as opinion polls or study results) there is another argument to be made.  Like we appreciate art, literature, and other humanities for their inherent beauty and the way they open our eyes to new ways of seeing the world, so should we appreciate mathematics similarly.

Mathematics teaches us (or can if taught and learned with aplomb) humility.  The superior attitude of some of those capable with numbers may seem to contradict this, but this may emulate from the sad way in which mathematics is taught.  An excellent author about mathematics in culture, John Allen Paulos, has often pointed out that math is taught and subsequently perceived as being about computation.  He says that this is similar to saying writing is about typing, and reminds me of a professor of mine saying, "To say computer science is about computers is like saying astronomy is about telescopes."  I will endeavor to avoid further digression about mathematics education, but will point out that when we tell people that they can find a certain answer following a couple basic steps we should not be surprised when they come to believe that they understand everything.

Mathematics is a harsh mistress.  When not teaching algorithms and their application (not a study of algorithms, which is rather enlightening, but instead essentially programming students in a manner shockingly similar to the way a programmer programs a computer to do specific computations), mathematics is about logic.  For the few reading that have actually done proofs, I feel this is a core of mathematics.  Working through with rigor new knowledge and insights from a handful of basic, known, accepted axioms.

What I learned taking a basic concepts of mathematics class (which with a name like that you may be surprised to learn was a junior level college course) is that this process is unforgiving.  One must be utterly cautious and unrelentingly precise.  One must avoid at all costs projecting one's desires, feelings, and possibly even intuition onto their work.  Instead one must choose to strictly follow what is known and established, to do what the axioms and previously derived theorems allow, and nothing more, and to consider every case and possibility

It is this, that makes me say mathematics is a Godly pursuit.  When I say mathematics is godly I mean that it is greater than ourselves.  We must be willing to practice humility and recognize laws that are beyond our instincts, hearts, and preconceptions.  The laws of mathematics do not bend to our desires because we feel they should.  Mathematics isn't a vehicle for our own ideas or agendas, but rather a manner in which we examine how we came to these and whether or not they require additional scrutiny.  Mathematics brings us to truth that we discover for ourselves but are independent form who we are.  Mathematics is bringing something beyond us and greater than us into ourselves.  This is what religion (like mathematics, when it isn't perverted into a degenerate form that is only good for frustrating students or wrongly justifying our preconceptions) does for us as well.

I will end repeating the refrain that mathematics teaches us humility, and this is what makes it at least nigh on divine.  To learn and to do mathematics is to seek knowledge and learn how little we know, what the limits are to our knowledge, and how easily we can err.  Is not such a pursuit godly?

Torn between two loves

Today is the release of Mass Effect 3. Like most major modern video games it costs $60 new, or $80 for the collector's edition. I haven't purchased it, though I absolutely love the series and can't wait to play the latest installment. My mom pointed out earlier that I do have the money. I still have some money in my bank account and credit on my credit card. I could buy it, but I'm saving my money for something else. Specifically, I'm saving for someone else.

I started dating a long time friend on new years day. The near 400 miles separating us are frustrating. We'd like to be together, but she lives in Salt Lake city and I'm in Denver. There's not much tying me down here, though. I'm planning to move once I have enough money to pay my student loans and other basic costs of living until I can find a job (which, after seeking full time work for about a year I worry will be quite a while).

So, I find myself torn between two loves. Many reading this might find my love for a video game frivolous or even downright foolish, so let me defend my already scorned love. The Mass Effect series continues developer Bioware's traditional of strong, character driven, intelligent writing. As discussed here, the game has raised questions about the nature of life and what it is that makes us who we are. It's been called the Star Trek of our generation, and I dare say that's correct. It's an original and epic space opera, in an unfortunate age where well written fiction, let alone science fiction, often loses out to the latest iteration of milf island, some dude dates fifteen women, or watch the train wrecks when it comes to entertainment. Mass effect is one of the games elevating the medium of gaming, a hobby I feel is at least capable of being very uplifting and intellectually engaging but is so often maligned (and not always unfairly) as being a waste of time at best or a mind distorting influence of evil at worst. Mass Effect enriches things I enjoy (science fiction and video games) by adding to worthwhile examples, and its success is a proof to those who finance entertainment that intelligent video games and well written sci-fi make money.

My love for my girlfriend is somewhat less easy to explain, but many more have written about love of a woman than love of a video game so I probably don't need to belabor that point. I've chosen to save what I can to hasten a long term reunion of me and my beloved. I can only hope that I'll be able to earn enough to actually go through with the move, and work hard enough to make it worth it when I get there.

Grow up

After working with kids at a summer camp for a little while I began to think about what maturity is. What is it that these kiddos lack that makes them kids. The answer I came up with was impulse control. The kiddos just weren't skilled enough in calming those emotional flare ups or dropping a silly argument. Hence, "Why'd you hit him?" "He said I didn't like marshmallows" or "Why're you so stupid, stars don't have rings. It's physically impossible" "Well, I dunno I'm gonna look anyway." "No, you're wrong, that'd dumb..." "Guys, quit fighting!" Of course in the discussion comes the inevitable acknowledgement: some adults don't have very good impulse control. I think we usually call these people jerks, annoying, downers, or some other of the vast collection of disparaging nomenclature. Controling your emotions is necessary for getting along well with others.
There is more rewards to emotional control than a good social life, though. It's a good life, and moreover, power to act for ourselves (free will, if you go for that term). Hear me out, Emotions are brought on by outside forces. A big scary bear makes us afraid. A bouquet of flowers makes us delighted. A new computer game makes us excited.
After those examples you might say, "but Devon, I like being delighted and excited. Me too, but it might not always be the best thing. If I buy portal (which I just did, finally, by the way) and I'm so excited I start playing and don't stop until the first week of school is over, effectively destroying any opportunity for academic achievement I have for the semester, that's obviously not good. I also loose the opportunity for other exciting experiences, such as learning and in the future obtaining a good job. If my shallow ex-girlfriend who cheated on me twice and continually criticized and spoke hurtfully towards me sent me flowers and I decide, "Oh she sent me flowers that's so nice I'm going to get back with her!" my net delight will be negative (I can feel myself getting back into physics student mode!). What if the flowers are indicative of a change of heart for this wanton woman, and renewal of relationship would do good for the both of us? Well, it still isn't smart for me to just run back. I might be happy and thinking the best of her, but wisdom dictates that I take care when reviving the connection we had. First, I don't know this is the case, and past experience indicates that it won't be good for me. Secondly, she may need me to be on guard. In reviving a relationship it would be sagely of me to go in stronger than before, ready for the maladies before heaped upon me, and setting boundaries and rules of conduct between us so that she knows how to improver herself around me and I am clear about what I want in our relationship. If learn to overcome these initial reactions and rule our feelings with our mind we can increase the happiness, peace, and whatever other good thing you want to put there (I was going to put joy, but it sounded too cute and trite "happiness peace and joy!").
So, let's be clear, emotions are good. Just like water is good. I see our emotional systems to be like indoor plumbing. There's a system of valves that we need to control, letting reason dictate the flow of each pipe. If we simply let each bubble over we'll quickly drown in our passing sentiments.