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.

Are We Ready for Post Scarcity? Part 3

So technology has brought us a new world.  The new technologies developed in the 20th and 21st centuries have created a world with changes as drastic as the invention of agriculture over 10 millenia ago.  This new world is awe inspiring in its productive capabilities.  Like the soviets upon seeing American grocery stores or backyard pools, those of us from the old worlds look in disbelief on the abundance the highly automated modern world offers.  Will that disbelief be an awestruck hopeful wonderment, or a horrified cringing at the dystopian nightmare on display?

What becomes of the human being, the individual in the post-scarcity world?  While objectively unanswerable, for now, science fiction and current trends can give us an idea.  Star Trek provides the most hopeful vision, a humanity that devotes itself to self improvement and growth, bravely venturing out to explore the universe or just starting a small restaurant to share the joy of old family recipes (like Joseph Sisko from DS9).  People engage in their passions and become the greatest captains, scientists, or chefs that they can thanks to the freedom from desire and from the struggle for the basic necessities of life.  While this optimism is one of the reasons we love Star Trek it doesn't strike us as realistic.

On the other side of the spectrum we see the 'dystopian,' or broken utopia, genre of fiction.  The lack of scarcity in information and communication enabled by the internet has made government surveillance and monitoring so easy that the protections for citizens seem to come only from law these days.  And that can easily fail, as the victory of the ACLU against ongoing programs of the NSA showed.  The NSA's activities have many shouting that, "1984 was not an instruction manual."  A conversation from the video game Deus Ex indicates another interesting, and all to realistic, future:

JC Denton: Some people just don't understand the dangers of indiscriminate surveillance

Morpheus (an AI system who is 'a prototype for a larger system'): The need to observed and understood was once satisfied by God.  Now we can implement the same functionality with data-mining algorithms.

JC Denton: Electronic surveillance hardly inspires reverence.  Perhaps fear and obedience, but not reverence.

Huxley's Brave New World gives us one vision of a post scarcity world that's also terrifying.  People are raised from conception to death to fill a certain role, with much of the population raised to lack mental faculty and drive so that they can be contented with menial jobs.  Innovation is suppressed if the rulers decide it doesn't support the economy.  The population is essentially drugged into compliance and acceptance of the system that promotes nothing but the status quo ad infinitum.  At least everyone has a job, though.

These uncomfortable futures are just fiction, for now, but sadly they seem to strike us as truer to reality.  One of the consequences of post-scarcity living is that power can evaporate.  It can also become much more concentrated.  Abuses by law enforcement that were once prevented by their sheer infeasibility now need laws in place to protect citizens (the supreme court decision on GPS tracking is a good example of this to add to the NSA's recent abuses of power).  However when laws are needed the question inevitably arises of who will write them.

The genius of American government is the idea of the powerful individual, that every citizen has strength enough to make their voice resonate in the halls of power.  The idea has caught on so strongly that it's easy to forgot how revolutionary and unthinkable this idea would be only 500 or so years ago when monarchs were the norm, and for basically all of human history before that when the strong took what they wanted without regard for whether or not the man they were taking it from cared to give it up.

The same power of technology that can eliminate scarcity could also conceivably eliminate freedom.  Corporate influence over lawmakers could barely be necessary if companies like John Deere, Apple, and Comcast continue along their trajectories.  Imagine the power the tractor company would hold if they were able to dictate whether or not their machinery were allowed to be repaired or you would just have to buy a new one to continue sowing grain.  Consider the power of a company with similar power over electronics and personal computers.  All the innovation and creativity in the world doesn't mean a thing if a company controlling the means of distribution for new products and stories can decide to refuse their service.

How can we dilute these powers, without only strengthening centralized government power, and while still providing opportunity and daily bread for the individual?  I don't know.  I have some ideas, but truly I can't say what I'd really do if I were ruler of the world, or even just the US.  What I can say is that no one else really can either.  There's a dearth of ideas and solutions floating around out there because we're not addressing the issue.

The idea of a post-scarcity economy and society is so revolutionary that it doesn't sound real.  Talking about robotics and computing replacing human beings as the driving force in the economy sounds like science fiction, despite the fact that we continually experience it as reality.  The whole issue is so massive and so out there that it's not addressed seriously in politics, and rarely in thoughtful conversation.  If this continues we'll find ourselves in a world clinging to obsolete social mores and struggling to make them fit in the modern world.  We can't let that happen, so let's think about getting ready for post-scarcity.

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.