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.

Technology, cheating, and the Augmented Mind

As a student I've been taking plenty of tests lately.  My university has a pretty good testing system and convenient testing centers and I'm a pretty good test taker so none of this really bothers me, but I have found the testing center policies interesting.  The fact that I have to remove my hat before going in is one.  Recently they've also disallowed the wearing of a wristwatch, almost certainly in response to the new smart-watch technology coming out.  While this is the right thing to do, it does indicate a need for much grander changes in both the way we do things as well as our thinking, probably especially in education.  Changes we are woefully unprepared for.

Let's consider the testing center again, perhaps as if you were the director of these.  We made the change for smart-watches so that they won't be used for cheating.  What will we do if Google Glass, or a similar project where data is displayed on a pair of glasses worn by the user, takes off and starts showing up?  If that technology becomes integrated into people's prescription lenses?  What about if those smart watches become smart tattoos?  What about when students start having direct neural interfaces integrating computers into the brain?  These problems are coming, and I think we can quickly see there's no easy solution, and maybe no solution at all to make a our current testing systems compatible with the existence of these technologies.

As my neuroscience teacher put it, most testing today is a simple demonstration of declarative memory.  This is to say tests usually require a simple recalling of facts, figures, or other basic knowledge.  However, the need for this to be done in the human brain is dwindling.  Facts can be more easily stored, more quickly recalled, and more reliably maintained in computer systems than in nervous tissue.  Why would we keep using cerebral circuits (that weren't really designed to do this in the first place) when we can use electronic ones?  The go to example is memorizing phone numbers, something many of us remember doing before technology made it an exercise in pointless exertion of energy.

Lest you think this is the pie in the sky omphaloskepsis of a futurist and science fiction fan, let me relay a story I heard from one parent.  He wanted to have his daughter writing letters, and specifically to do so using some specific vocabulary.  Shortly after he heard his daughter speaking out loud while alone in her room writing the letter.  Listening closer he realized she was using the voice recognition feature of the tablet/smartphone to simply ask for the spelling of the appropriate words.  This was much to his disappointment, as he was expecting her to look the words up when writing them and learn the definition along with the spelling.  That's how big a change something as simple as voice recognition is making.

A future where traditional testing is pointless seems on the horizon.  How education will or even can deal with this is unclear.  The problem with leaving our traditional testing is that other methods require more work to evaluate, and usually are less objective which can be a big problem for admissions tests like the MCAT.  The only solution I've thought of is an increase in internships and apprentice work, but whether or not this is feasible is unclear.  I know the major reason the radiology or medical laboratory programs at my school can't admit more than about 40% of applicant students is because they only have so many slots for clinical rotations available.  It could be damaging to the economy to have the influx of cheap or free labor that having five interns or apprentices to every one trained employee might mean.  The problem is a big one, and sadly I haven't seen it given all that much attention.  Let's hope for and work toward that changing sometime soon.

From an Aspiring Medical Professional

I've always been a scientist.  Some of my earliest memories are wanting to use beakers, test tubes, & microscopes in school.  My mother tells me that one of my favorite toys as a child was an old radio I was allowed to disassemble and rebuild, being fascinated at how the pieces fit together.  I've always seen science as exciting and fun.  For most of the time that I understood the concept I've seen it as a noble pursuit as well.  "The glory of God is intelligence," I was taught, and science is a rigorous pursuit of understanding.

I've learned since then about the very human nature of this endeavor.  Learned things like how Newton's preference for a 'corpuscular' or particle theory of light, rather than the wave theory which works better, probably set back the field of optics a century or two, but few wanted to propose ideas that would dare contradict the great and powerful Newton.  I've learned this about religion, philosophy, sports, families, and just about everything else humans do as well, though.  These days science may have trouble acknowledging its limitations, but it does good and improves the human condition.  And yet the ranks of those who share this view are suffering loses.

This seems mostly in the field of medicinal and health sciences.  This rarely used to bother me, but it is more and more lately.  Maybe it's because I'm getting older and the issues are closer to affecting me and involving choices I'll have to make.  Maybe it's just because things that were more fringe in the past are getting talked about more these days.  Maybe it's because part of me agrees that this field of science is a lot more blurry than the physics and mathematics I originally studied, but entering into the field I'm seeing the strength of the science.  I'd be remiss not to have mentioned these possibilities in a writing about science, rigor, and emotion, but I don't think they're the reason.  At least not the primary one.

I am an aspiring medical professional.  I'm going into radiography or clinical laboratory science, depending on which program accepts me and a few other factors.  I feel like scientific thinkers, which would include many medical professionals and certainly myself, rarely make effective arguments that would entice someone not scientifically inclined to rethink their ideas.  This is likely because anecdotes, emotional pleas, and pithy quips will not change the fundamental forces of nature and therefore aren't the first thing reached for in scientists' mental toolboxes.  So it feels odd for me to speak about my emotional and personal reactions in the context of understanding biomedical science, but it may be just what some need to hear.

There always seems to be an edge of accusation toward the medical profession by those that eschew its methods.  It's difficult for me to say this as I don't believe it's intentional, but it is the truth.  The message is that the medical profession, and therefore medical professionals, is a bumbling ignoramus unwilling to understand the simple truths that should be instinctively understood, a shadowy or scaremongering elite seeking only power and control, or an uncaring power more interested in processing patients to collect their checks than healing them.  It may be some combination of the three, but these are the primary narratives with their implications laid bare and made plain.

I believe they are all wrong, but moreover I know they are all insulting.  I think this might be why I've been more affected by those who leave the ranks of accepted science for other conceptions of fulfilling medicine.  The secret message in those actions, words, and thoughts are that I don't care about my patients.  I do care about my patients, and I don't even have any yet.  I study hard and ensure I understand the concepts of my classes because I worry about making the wrong call and endangering someone's health.  I've listened to opposing views, considered the ideas, and always been unconvinced that those methods and practices would best serve the sick or the healthy.  I want to get paid for application of the skills I'm acquiring, sure, but I did when I worked other customer service positions as well and was still driven to serve the client.  When I see someone taking medical risks I'm annoyed because so often those risks are unnecessary, and I care about them.  So, from an aspiring medical professional, please reexamine your ideas if you're forgoing modern medicine.  Please give me and my ilk the benefit of the doubt and some level of trust.  We're absolutely doing our best to deserve that much.

Expressing Curiosity in Science

As a student of the sciences, mostly physics and recently medicine, I often will get caught in discussions of 'what is science?' as in a recent lab class.  I often resist engaging in these because I feel they too often are trying to promote idealized views of this particular human endeavor.  The humanity of the enterprise is forgotten in trying to give it good PR.  Most recently I did have one thought on the subject that seemed of value though: science is one expression of the curiosity of mankind (and remember man in this context is gender neutral).

We have an interesting relationship with curiosity.  The most well known phrase in regards to the subject is, "Curiosity killed the cat." I like to use the snappy rejoinder, "Well we better try to satisfy curiosity before that psycho goes off killing small animals to get their jollies then," but I recognize that the implication the phrase carries is to take caution with exploration and intuition.  As should be obvious to the reader at this point I don't agree with this mentality, but that said it's never wise to throw caution to the wind entirely and we should certainly ensure that our actions properly reflect  the correct balance of our desire to know something and other desires, such as comfort, safety, and community.

I still think that on balance curiosity is a virtue.  I believe in the freedom of information, an understandable order and structure underlying the universe at large, and that challenges to one's thoughts and beliefs will eventually improve them if faced head on and not ignored.  Curiosity lets us promote and explore these things.  Consider what the opposite of curiosity might be.  A quick look in the thesaurus brings up disinterest, indifference, perhaps even apathy.  Does anyone really want to be with people or build a society with these qualities?

Science is one way in which we express our curiosity.  It's perhaps the simplest, being based on straightforward observation of a community.  Laws and theories are only useful in as much they can make verifiable predictions and only believable in as much as they are supported by data and experiment.  This does make science somewhat limited in scope as most will recognize that there exist things that simply can't be proven one way or the other, but the pragmatic and skeptical mentality is a powerful tool for any thinker.

Science is of course a human enterprise, though.  This expression of our curiosity is subject to the same forces that might make a desire for self improvement into greed or a longing for love and community into exclusion.  Having guiding principles in a great human venture never means we follow them perfectly, or if it does it probably means we're losing sight of other virtues.  The guiding virtues of science - observation, falsifiability and testability, and of course curiosity - will indeed help us in our endeavors to become virtuous.