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.

Fix it Mommy!

Over this last weekend I had the opportunity to see a number of my cousins, many of which have young children.  One moment in particular stuck out for me.  One of the mothers asked for some sort of cream or lotion to give her child.  The child specifically wanted what I believe was an anti-histamine cream to relieve some itching, but the mother knew that anything with roughly the same physical properties would fill the child's real need; to have their problem attended to and be given a simple solution.

Children are obligated to go to their parents to fix the majority of their problems.  In infancy they have only the one signaling mechanism to do this, crying, and deploy it whenever they experience discomfort or want so they can obtain the attention of parents that will then fix the problem.  As children get older parents teach them more sophisticated signaling mechanisms (such as 'using their words'), but the drive is the same, get the attention of mom or dad so that they'll put in the effort to fix my problem.

I also witnessed the impotent rage and anguish children experience when this process fails, or even more horribly when mom or dad suddenly turn and become the cause of vexation (like being told to leave the swimming pool).  The wise parents I was with simply weathered the tantrums and softly prompted their kids to learn to manage their emotional responses with greater aplomb.  The lesson will hopefully be learned by these children, though it will probably take a few more years of experience and cerebral development.

What struck me was the inborn drive represented by this, and the realization of how often this thinking expresses itself throughout society.  We are constantly turning to figures of authority and power hoping that with their attention and efforts focused on us our problems will get fixed.  We get angry when those we think are supposed to fix our problems do things that stifle our enjoyment and comfort.  At another point I also discussed with my father, a professional psychological counselor, how so many want a pill to fix their problems and prefer that solution despite numerous benefits therapy has over drugs.

We can be active and fight to better our lives when possible, and feel the disappointments of unfortunate but unyielding circumstances without letting that sadness or anger hijack our mind.  I'm taking a class in pharmacology over the summer and the lesson that comes up over and over is that all drugs have side effects, and therapy is always just a matter of handling one thing with a cost that's deemed acceptable.  As Thomas Sowell put it, "All that goes with the territory, that is with a universe we did not make having constraints we cannot escape, and offering only trade offs however much the intelligencia and the politicians proclaim solutions."

The realization that there are no easy solutions for the biggest problems in our lives and that we're doomed to an eternal existence of managing (as opposed to fixing) the obstacles in our personal lives and our community is sobering, indeed.  It is also what we must accept if we want to truly gain maturity beyond the child yelling, "Fix it, mommy!"

Thirty Years

Yesterday was my thirtieth birthday. As I leave my thirtieth year of life and enter my thirty-first I reflect on the passed year.  Year thirty feels as if I've been a plane that's waited at the gate, taxied up the runway, and taken off for a new destination.  Here's the highlights:

• Working at inthinc : I continued my job at inthinc technology solutions for the first part of the year.  This time taught me once again the importance of good management.  Our last manager was very skilled at keeping the support team of which I was a part happy and feeling valued within the company.  During the first part of the year we had no manager and a number of internal conflicts arose within the team as well as numerous difficulties arising from a lack of effective interfacing with the rest of the company.  Our new manager, when hired, eventually turned out to make promises like a politician, fail to inform us about and connect us effectively with the rest of the company, and make the talent feel undervalued. I was the third person to leave the team as the burden on our team increased and feelings of valuation decreased.  After leaving the company I continued to hear of hardships and found the company was losing money and talent at an alarming rate, though it seems to have stabilized at this point. I have a number of good friends from my time there, but am happy to have gone.
• Returning to University : Leaving inthinc prompted an overall career change.  I had noticed that the career trajectory in technical support would take significant time to advance and might not lead to a place I really wanted to be.  Looking at what field might be related to my previous scholastic experience in physics I found that radiology is something that would probably take about as much time to train in as it would to advance in my current work, had similar job demands at higher pay, and ultimately would be more fulfilling and interesting.  I enrolled at Weber State University and started attending classes. I was reminded how much I appreciated the university atmosphere and learning new material.
• Entering Medicine : Preparing to enter the field of radiography I've been learning about the medical field generally as well.  I trained as a phlebotomist and am making arrangements to test for my limited x-ray machine operator's license.  I have been fascinated by the challenges and nature of the medical field. There's an intriguing intimacy to healthcare that makes me feel a great deal of responsibility toward patients. I never thought that biochemistry would hold any interest for me but after studying it (in part at least) for a semester I've completely turned the corner and am engaged by protein structures and metabolic pathways.  There's clearly a lot to learn and do in this field and I'm eager to continue exploring it in year thirty one of life and beyond.

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.

Our Data is Who We Are

 The physical is becoming less and less important in the modern world.  Sure, there will always be a need for physical mediums (after all "There is no such thing as immaterial matter. All spirit is matter"), but information is what reigns supreme in importance.  This has always been true, in many ways.  As Carl Sagan said, "The beauty of a living thing is not the atoms that go into it, it's the way those atoms are put together."  In another way, humanity has been marching toward this for ages; Since the invention of writing a stone could be transformed into the law of the land or God, a history of a people, or an agreement between two parties.  The invention and standardization of money intensified this.

The idiom that you can find out a lot about a person by going through their trash may still be true, but it's been found that with a handful of data readily made available people can know exactly who we are (in this study 4 locational data points were enough to identify 95% of participants).  While it's (probably) true that you wouldn't be you without your physical body, too often we forget that we wouldn't be who we are without our memories, habits, and interpersonal connections-all of which computers are increasingly involved in and therefore archiving.

As a Verizon wireless customer I was devastated to see this report from the Electronic Frontier Foundation surveying different companies and what measures they were taking to protect users' privacy.  I've known for a while that Verizon was kind of a scumbag company, managing to continue living only because they've acquired a great deal of infrastructure.  When (also scumbag, when it comes to users' data) companies like Comcast and Facebook (I'm not including Google even though many might have worries about the amount of data they collect because they did manage to collect 5 out of 6 stars in this survey, and I genuinely appreciate the company) as well as the two lower end Apple and AT&T still manage to find some way in which they can protect users' data rights are still beating out my carrier, I worry.

I'm seriously considering leaving Verizon, and would probably side with Sprint.  The financial, coverage, and overall convenience implications makes me hesitate, but I really feel like making sure a company that isn't making any effort to protect my digital self shouldn't be supported by my money.  I'd love to leave Comcast for the same reason, and may look into campaigning within my complex to get a different service provider.  The power a service provider has in my life is unnerving, considering how important my data is to me.  After all, in a very real way the data about me is who I am.

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.

Waiting

"Patience is a virtue," everyone says.  Often one hears a response along the lines, "Yes, but it's one I don't have."  I feel like this response misses the mark terribly and perpetuates the foolhardy idea that our virtues (or vices, often) are just something we are born with and will end up living life according to.  It undermines the idea that we humans are free and have the power to act for ourselves, debasing man to nothing more than an animal, or even the earth, water, air, or other elements of nature.  Since, as you may have noticed, the author finds this idea somewhat repugnant he will often retort with something like, "And we must learn to develop virtues."

Patience is, or at least is often perceived to be, how we handle waiting.  Do we sit quietly, do we fidget, do we pace up and down?  There has been an odd change recently that has caused us to think many things should happen instantaneously.  When I worked as a camp counselor the employee use computers were very obsolete and of course ran quite slowly.  Rather than disparaging the frustrating situation I came to refer to these as the "Zen computers."  I try to take this sort of attitude toward a lot of waiting; standing in a line, downloading a webpage, or standing at the bus stop can be great opportunities to think and observe our thinking.

Often waiting frustrates us because we feel such a drive to get our next task finished or such desire to have whatever we'll get after the wait.  I've had to adjust lately to some of these feelings myself.  I recently changed from a company that would give me a weekly paycheck to one that pays every two weeks.  This means I have to wait longer when I want to make a payment on my student loans, credit card, rent, cable bill, or anything else.  I've had to do slightly more planning ahead, but the bigger deal is becoming comfortable with things the way they are until I have the resources to change them.  I think this is the greater principle here.  Often we get frustrated, aggravated, or just plain angry when we're forced to wait because it's such a clear signal that there's something we can't control.  Facing our limitations is always humbling, and many don't wish to be humbled.

Lately I've also been waiting to get married.  This has been one of the most interesting experiences I've had in learning to wait.  I feel such deep desire toward my beloved as well as a certain sense that I won't be taking the next step in my life until the wedding day has come.  I'm learning a lot when about enjoying the experiences I'm having even while wanting so much more.  I think this is what we're really seeking when we talk about learning delayed gratification.

It's easy to view waiting as something onerous and obnoxious.  It's common to equate a wait with a difficulty.  I think waiting is a great way to learn, especially about ourselves.  Know thyself, the saying goes, and while doing things is important we also need to take time to get to know ourselves in a more intimate setting.  Waiting is a great way to do that.