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.

Imagination and Knowledge

After my last post I decided I want to write another one this month, since I like to cool off and give any readers I might have a break when I go on tears about technology, law, and society.  I didn't have a good topic that I wanted to talk about, though, so I asked my wife what she thought I should write on.  She provided a one word prompt: imagination.  I decided to go with this, but having something so broad I needed to keep looking.  A few internet searches later I happened upon some Einstein quotes around, Imagination is more important than knowledge."  In that way I have I said to myself, "¿Is it?" and then I realized I had a topic for a post.

I think considering imagination and knowledge more important than one another is actually a little misguided.  They're different entities that have different purposes and bring differing benefits to a person or society.  It's like saying hammers are more important than saws or potatoes are more important than chairs.  And we can often get by with only one.  But, these are two forces that gain the greatest power when working together.

Knowledge is a foundation.   Knowledge tells us how the world and things in it work, how to do things, and how things are connected.  Imagination gives us the capability to see how these facts could be different, improved, or superseded.  But using imagination rarely can make a strong impact if we're without the knowledge to back this up.  Knowledge lets us reasonably examine the ways in which the things we imagine might play out, so that when we try to put those things we imagine into reality the chance that we're successful is higher.

My love for Star Trek was recently re-kindled by a collection of online reviews of works in the franchise and one thing that's been striking is that one of the most impressive things about the franchise was its ability to imagine the future in a very different yet very reasonable way.  Social issues such as race, ethnicity, and sex becoming less important to a team that works together.   Also, amazingly, the science of instantaneous point to point transportation, faster than light travel, and futuristic weaponry (though it was changed later, the original meaning of the term "phaser" was "photonic maser" which, while actually redundant since the microwaves a maser produces are made up of photons, points toward the laser which does indeed exist and could be weaponized).  Many of the high points of the series' are when this works to add believably and a feeling of reality to the impossible,and failures of the series often occur thanks to imagination being backed up by too little knowledge.

Sacred Sexuality

"Give not that which is holy unto the dogs, neither cast ye your pearls before swine." taught Jesus in the sermon on the mount. Casting pearls before swine is one of those phrases that floats around today but is seldom given the consideration it deserves. On my mission I felt like I was walking a precarious line between sharing the gospel and casting pearls before swine.  But anyway I'm not writing now to talk about sharing the gospel. I've wanted to write for some time on sex, and this scripture came to mind when thinking what to write.

Sacred sexuality is one of those new-age sounding things that usually gets thrown around by those that want to talk about how great sex is.  That somewhat more snide than I intended remark aside, I think sacred sexuality is entirely real.  Sex is something sacred, and that's why in my life it's reserved for marriage (which is also holy).  Often in Christian circles the holiness of sex is directly related to the ability to bear children, and while I think we should hold the same gravitas for the acts of creating life as we do to destroying it I don't feel that this is what makes sex something holy.

So what is it that makes sex sacred, then?  The words sacred and holy both derive from the idea of setting something apart, reserving something for a higher purpose, or dedicating something to a greater cause.  Sex for me is something reserved for marriage.  That imbues it with the high purpose of strengthening marital bonds and by extension the family.  That makes sex a way to study selflessness and caring for another (without abnegating one's own needs or desires in the process).

I own a book of erotic myths and legends and read one together with my wife the other night.  The one we read was (perhaps a little bit surprisingly) rather tame with almost no mention of sex but rather an extended poetic meditation on love, longing, desire, loss, and union.  Although when reading we might have been looking to partake together in something a little more saucy, I'll also say I actually really liked this little legend of a lover comforting himself that his "beloved other" was not truly lost because they had become one soul.  Sex is a part of that, and that makes it sacred.

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.

What is Marriage?

I'm getting married soon, and that could mean something different to every person I tell that too.  I recently discussed with a co-worker about how difficult it is to establish a mutual understanding of what marriage means, so in the spirit of creating a better understanding of what I'll be doing I want to express what marriage means to me, as well as putting forth some general ideas that may be useful to anyone in understanding the concept of marriage.

Often marriage is is equated with lifelong commitment, but I think there's a better way to understand marriage.  Marriage is a commitment that  goes beyond the couple.  It's when two people make a commitment not only to one another but to a third party.  The details of who or what that third party is define the greater details of what marriage means to them.

If we marry with a government, it largely means they now have an array of legal rights regarding each other, and that they cannot fully dissolve their relationship without consent returning to a representative of the government.  Often the third party will often be God or a church, which introduces a spiritual element into the relationship.  This lends important understanding about marriage because it goes beyond being committed to one another.

Yes, many people are committed and plan to spend their whole lives together without ever needing to get married.  That's one choice, people can also choose to express this through marriage.  I feel that marriage is an option we employ when we feel the need to elevate our relationship above the two (or sometimes more) people in it.  Marriage is a declaration that we are not only committing ourselves to another, but to the betterment of our society, our people, or our God.

I'm getting married because I want the benefits granted by government and God.  I want to be with my wife for this life and the next.  I want to be recognized as one who cares for her and has entwined his life with hers, in finances, health, and the search for spiritual salvation and perfection.  I want her to know I won't leave her, and have the guarantee not only of my words but a contract with greater powers to which I will have to go if I ever did.  I want to work with her to better ourselves and the world in which we live.

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?

Ramadan: Day 10 (written on 21st of August)

As a sort of spiritual experiment I've been keeping Ramadan this year. Today was day ten, and I thought I should record some of the thoughts and experiences I've had so far. What truly inspired me was my morning prayer today. Mornings in general have been an interesting part of Ramadan since I usually sleep in well past sunrise. I still have, often enough, but to eat before the daily fast begins I've woken up early once or twice. Once before today was a very nice experience, but more frequently I've woken up, eaten a breakfast, and then gone back to sleep. Today a woman I've been getting to know also wanted to begin waking up early in the day, so we made plans to call each other in the morning. I talked to this fine woman while eating a modest breakfast yogurt and oats (and some leftover brownie too) and watching the sunrise. One of the topics of discussion was the morning. The morning is different. Evenings and nights are still very active for modern Americans. Mornings, especially as early as before sunrise, are very quiet and still. This made it a nice time to speak with a new friend, and it has also been an ideal hour for my introspection. Watching the sunrise has been very nice. First just because it's so novel to me, seeing as I usually loath being up before the sun is, but more importantly just to appreciate nature's beauty.

This is the second time I've prayed during sunrise over Ramadan and it's been spectacular both times so I should really work to do so more often. Today was particularly powerful. These prayers are great because after waking up and eating breakfast and then watching the sunrise I've shaken off the tiredness and am alert enough to feel the Spirit of God and speak meaningfully with Him. I did so today near the end of the sunrise, I knelt down for prayer and when I rose up the sun had unhidden itself from behind the horizon and sunlight spilled over me as I lifted myself up from prayer. I thought this a exquisite symbol for the Holy Ghost's presence that I also experienced.

One of the things about prayer, faith, and ritual is that mundane things in life become holy. The sunrise, while always lovely, today was a testimony of God's greatness, power, mercy, care, and love. My fast has been food only, rather than a full on traditional food and water fast, making the water I drink a sacred reminder of the Living Water which slakes my thirst for meaning, justice and righteousness in life. I hope to continue and improve upon these experiences as I continue Ramadan.

Thoughts from the Airport

I love airports. An airport is an exciting nexus of modern human existence. A coming together of people, people on journeys. Some leaving to see others for a joyful celebration, some doing the same but for a somber purpose. Still more arriving, perhaps wearied from their voyage and excited to meet friends and settle in at their destination. Or excited to finally be in the place to where they anticipated coming.

They're grand testimonies to modern technology, and while some worry and fret over technologies march forward I marvel and embrace what it's brought us. It was 107 years ago that man first lifted himself from the ground with nothing more than ingenuity, effort, and luck. And now we've mastered the craft so well that anyone can do so for the same price as an expensive piece of clothing. We build what are cities unto themselves to support people taking to the skies day by day. That is what an airport is.

The airport I'm at now is perhaps not one of these, being smaller than where I arrive, the Denver International Airport, but it still excites me. Today I played a game with myself. I tried to move slowly, sauntering through this buzzing hive of humanity. Airports usually excite me and I energetically pull keys and shoes off at security checkpoints, forcefully drive forward toward the gate from which a few tons of steel, silicon, and modern aeronautics will carry me to wherever I wish to go in the world, and then arrive somewhat disappointed that I've been so efficient only to arrive early enough to wait. I still arrived early enough that I've spent about an hour and a half waiting, but it's certainly been enjoyable. The air conditioning has deceptively made the sound of a waterfall in the section of seats next to mine. It's rained and a few brilliant blasts of lightning and deep peels of thunder have been mine to enjoy. Most of this time though I've used to read and, now, to write.

Physical Attraction-not the kind between an electron and a proton if ya know what I mean

When I was younger, probably entering puberty, I came to believe that physical beauty, by which I suppose I mean sexual attraction-just to be perfectly clear, was largely a societal construct. Think about it, the Venus de Milo would be "plus size" and even Marilyn Monroe would be a size 12-16, a far cry from today's "supermodels" whose dress size approaches or is the additive and multiplicative identities of the integers/real numbers. I think it's probable that today's nice skinny figures would be considered emaciated skeletons by earlier standards, especially in those societies that valued the ability to reproduce, looking for "hearty women with child bearing hips."
My point here is to ask how much physical attraction is societal, though. Obviously sexual attraction to women, in male's case and vice-a-versa, is natural inborn desire used to perpetuate the race, but I wonder if the specifics are essentially manufactured. If you like women with big breasts, is there anything to that other than a sort of societal brainwashing? To be truly free of being a mindless follower of the crowd, must we throw off the chains of what physical characteristics are sexually attractive and look deeper into people's souls to find our attraction?
People often speak against this idea when I present it, usually with the line, "There has to be some physical attraction in a romantic relationship." Well, I agree (duh) if you find your partner a repulsive specimen of the human form that things are gonna be rough. However, physical attraction is mental, and often changes according to our opinion of someone. One may have heard that confidence is important to looking good, and it's true. Many people have probably experienced a growing attraction to someone as they got to know them better. One slowly overlooks flaws and focuses more on attractive aspects, or vice-a-versa according to one's opinion of another.
I'm sure folk have opinions on this, and I'll be interested to see the discussion that ensues.