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.

Sharing an Idea

Since I just got married I've been posting about marriage, relationships, and the like lately and I've seen an interesting thing happen, people responded.  I got comments, page views, and people telling me how much they liked my last post.  It's always nice to hear feedback from others and find out people are actually paying attention.  Still, part of me is actually a little disheartened by this surge of interest, because it carries an implication that people didn't read, or just plain didn't care about what I was writing before.

I wouldn't have predicted my newer writings would have eclipsed some of my others, because I find them more personal in scope.  Curiosities of my personality, musings on relationships (of which there's already enough literature to fill several libraries of Alexandria, and what I bring surely cannot be that novel), and altogether introspection on how I feel during such a pivotal moment of my life.  Maybe I should be honored and awed that others care about enough that they love my introspection.  Maybe they feel they're getting to know me better through my writings, and that's what engages them so deeply, and again I should be cheerful to know people like getting to know me.

But perhaps that's also just it.  Yes that personal side who loves his beautiful new wife and was eager to marry her is there.  Yes, I have thoughts and feelings about romance and love like most everyone else.  Yes, I am relate-able in those ways and those are all important to me.  There are other things that are deeply meaningful to me, though.  These are things that run from boring to meaningless to spurned to intimidating (and therefore avoided as much as possible) to much of the population in which I live.

Often what I write blog posts if not necessarily to change vernacular perspective at least to offer a different one.  I find topics of science, mathematics, and technology - and especially the public's interaction with these - of immense importance.  These are the ventures of human endeavor that will shape the future to which hurtling toward us faster and faster every day (ponder a moment on the technologies changing the way we communicate and relate to one another that have come to fruition in the last ten to twenty years) and the lijera (Spanish for lightness, but possibly carrying an extra connotation or two that made me want to use it in place of an English word here) with which people take these today is distressing to me.

I was once asked by an aunt something like, "What's it like to be as smart as you are?"  My answer was a jocular but wistful, "Lonely," and then by way of explanation, "When I talk about something that I find fascinating and then see the eyes of whomever I'm speaking with glaze over what do I do?  Pretend something important to me isn't or speak without regard to a fellow human being."

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?