Monthly Archives: December 2013

Books Culture Music

Humans Are Great 6: Stopping Time with Anton Bruckner and Knut Hamsun

“One of the things you’ll never know without God is what it feels like to be completely outside of time, submerged in something both boundlessly immense and profoundly personal.”

It’s one of those things you hear at the end of a long, circular night – all of the standard arguments and counterarguments have been batted about the table, all the requisite statistics recapitulated, and, bleary-eyed and hoarse, the real issues that separate believers from non-believers start making their quiet voices at long last heard.  And what those issues often amount to is a personal unwillingness, on both sides, to renounce a whole category of human experience as merely the phantoms of neural fancy.

For the religious, that depth of feeling that they get when they feel Jesus over their shoulder must be real, and they cannot comprehend how we stumble through our day without its eternally fortifying presence.  For us, that wild rush of pure intellectual freedom that stands before the towering maw of entropy and says Go Ahead, Bring It, and which we can’t imagine another thinking creature mangling in the name of comfort.  These are experiences that each side thinks as unknowable to the other, experiences that keep them reconciled to the rest of the intellectual contract they’ve signed.

The experience of altered time is one I hear rather a lot, and have always felt as something well within the confines of secular culture to accomplish.  Some of my favorite bits of artistic production revolve around just this ability to take our experience of time and twist it, alternately suspending us in pure timelessness or otherwise diverting our sense of its pressing linearity.  For the former, you can hardly do better than the symphonies of Anton Bruckner.  There is a great deal of wonderful classical music out there, but no composer has his ability to craft a tonal landscape that simply arrests time in its tracks.  You stop noticing the things that Desperately Need Doing, stop even really analyzing the music as music, and instead just let it grow over you, an insulating layer of lush moss that keeps space and time at bay for an hour.

You can really pick any symphony to feel this (though 4, 6, 7, 8, and 9 are perhaps slightly more effective than 1, 2, 3, and 5), but for me it doesn’t come any better than the third movement of the 8th symphony (and if you’re of an impatient sort, but want to hear an absolutely perfect musical moment, fast forward to 1:58):

I would pit that against the most intense moment of prayer any day and never feel myself the loser.  But it’s perhaps easy to hypnotize with music, to do so with words on a page is a whole different level of artistic sorcery.  And precisely that is what Norwegian author Knut Hamsun (1859-1952) achieved on a regular basis throughout his long career.  From the scratching, morphing staccato of Hunger to the sense of cyclical death and regrowth in The Growth of the Soil to the drifting euphoria of Wayfarers, Hamsun is the guy to go to when you want mere sentences and paragraphs to change the very beat of your heart, the way you walk through time after having put the book down.  And not a word of it relies on the neurological cocktail that religion leans on to pull off its hallucinogenic spurts.



We are, persistently and mostly fortuitously, creatures of linearity.  We armor ourselves in the past to deflect and absorb the shocks of an unknown future we cannot reach fast enough.  But, from time to time, it doesn’t hurt to place ourselves in the experienced hands of one of our great creative minds to know time’s flow in a way that defies the strictures of pragmatic necessity.  Religion can do that, but never forgets to charge heftily for the pleasure.  Bruckner, Hamsun, and the dozens of others who found in them models for a new temporal sense in art, give us variations upon lived time of exquisite refinement, and the only criteria for admission is Being Human.

Philosophy Science and Math

William Lane Craig’s Seven Reasons for God’s Existence

William Lane Craig has a surprise for us.  In the newest (Nov/Dec 2013) issue of Philosophy Now, he announces that, not only is philosophical theism not dead, but it is actually the most vibrant part of modern American philosophy, beating archaically positivist atheists back in chaotic retreat whenever it unfurls its revolutionary new arguments for God’s existence.

And what’s more, Craig confidently claims, in the space of four pages he is going to present us seven of the freshest, most undeniable arguments that point towards the existence of God yet produced from this flourishing legion of great minds.  I admit to being rather excited to read something new at long last, something that would really shake the foundations of my weaker assumptions and force me to grapple again with my philosophical principles.  Sitting up with anticipation, I proceeded to the first of these brand new, entirely irrefutable arguments….

And it was the First Cause Argument, stated substantially the same way it was when its inner contradictions were revealed as such a century and a half ago.  Gaze at these two initial steps, if you would:

1.  Every contingent thing has an explanation of its existence.

2.If the universe has an explanation of its existence, that explanation is a transcendent, personal being.

Imagine my disappointment that, not only isn’t this version an update or improvement on what has gone before, but it slips into the non-qualitative equivalence trap that the better versions of this argument have at least attempted to address for a while now (namely, that the first step sets up an analogy, but the second introduces (or, “slips in” if you’re feeling uncharitable) a qualitatively different event that breaks the chain of analogical reasoning).

Fine, then, the first argument doesn’t precisely break revolutionary ground.  Perhaps the second will:

2. God is the best explanation of the origin of the universe.

Or, he could just restate the structure of the first argument with a little bit different evidence.  Which is what he, in fact, does.  The new evidence is the Vilenkin Theorem that the universe must have a definite beginning.  Again, it’s a modified Aristotilean argument by analogy, and again the same problem of hidden qualitative distinctions rears its head.  We can give him that it’s possible the universe had a definite beginning and that cyclical or chaotic models might ultimately prove untrue.  But that doesn’t give quite the stretch-room he needs here.  He needs creation from nothing to be qualitatively similar to the re-configuration of existing matter that usually brings “new” objects into existence, otherwise the analogy doesn’t work, and unfortunately those two acts are about as dissimilar as can be, and to argue from the prerequisites of the latter backwards to the implied prerequisites of the former is just irresponsible.  And that’s been common knowledge for a while now.


Moving along, the third and fourth arguments, because they both come from the same place and suffer from the same problems:


3. God is the best explanation of the applicability of mathematics to the physical world.

4. God is the best explanation of the fine-tuning of the universe for intelligent life.


Argument three evinces a distinct disregard for the work in the philosophy of mathematics done over the past century.  It over-emphasizes math as a static body of knowledge and fails to mention anything about mathematics as a method, its assumptions and techniques, and how those might or might not be effective at engaging with the universe.  Only by confronting the research done in that field can you even start making statements about how “coincidental” the correspondence of certain parts of mathematics as they are currently understood with the physical universe as it is currently understood might be, and how much of a miraculous intercession is necessary to cover that supposed coincidence.  To make these statements without mentioning the work of Pickering or Plotnitsky is to hold up an easy and uncomplicated ideal in place of messy reality, which is lazy at best and consciously deceptive at worst.


As to four, it’s the Sweet Spot argument writ universal, and, of course, the problem with it is that it is devastatingly myopic.  He says that the constants of the universe are so arrayed within the thinnest sliver of possible values to make life as we know it possible, and therefore the life-sustaining nature of the universe is a sign that it has been designed for life, by somebody.  God.  Ignoring all the more obvious problems of circularity that the argument has dragged with it for the better part of a century, what I always find a curious oversight is the fact that, just as surely as human life exists in this universe during this slice of time, so will it surely not exist in another slice of time, not too far removed from our own.  The sun will explode, and even if we escape that, there is an expiration date on matter’s cohesion in an expanding universe that is running a race with entropy to wipe us out no matter where we go.  The universe is a short-term life sustainer, but a long-term life destroyer.  To favor the former aspect over the latter is understandable if you think that Jesus is going to show up and whisk everybody away before all of the bad stuff happens, but if you’re starting from a blank slate of belief, the construction of the universe seems so overwhelmingly against the long-term existence of humanity that only a God with the sadistic instincts of a house cat would have so designed it.


5. God is the best explanation of intentional states of consciousness.

This argument supposes that mere materialism cannot account for the Aboutness of human thought.  It absolutely can, and a fair number of the neurochemical pathways that allow us to access and coordinate memories in conjunction with received stimuli have been mapped in loving detail by an army of quietly diligent heroes whose names we’ll never bother to know.  Yes, thoughts seem like they are very subjective and outside of your mere physical matter.  But they’re not.  They’re a chain of chemical reactions pushed by other chemical reactions, and our experience of believing ourselves to be having a thought is itself, you guessed it, a recursively sustained chemical reaction, a war of inhibitors and neurotransmitters all galloping along with our primate DNA to sift through the world’s offerings for the most important bits of data.  But, hey, at least this argument is merely five decades old.  So, progress.


6. God is the best explanation of objective moral values and duties.

This was CS Lewis’s big starting argument in Mere Christianity, back in 1943, and of course goes back before then.  It was a somewhat forgivable argument for the forties, but is utterly indefensible in the face of what we have learned since about the origins of empathy from primatology, and of the nature of our decision pathways from neurobiology.  We have discovered more and more instances of supposedly Human Exclusive moral behavior in our research of animals, pushing the uniqueness of our ethical behavior into a narrow scope so obviously linked to what came before that to suggest the need for a divine source is to be astonishingly unwilling to engage with the past half century of research on the subject.

Thence to the big finale…

7. The very possibility of God’s existence implies that God exists.

Yep, the ontological argument, that revolutionary new idea from the eleventh century.  A part of me was hoping that Craig would save his most daring and interesting argument for last, and the groan of disappointment I uttered upon reading that line resonated through the house.    Craig adds nothing we haven’t seen before, and this argument has been dealt with too many times to even bother with a recapitulation of its manifold flaws.


What started off with bold and heady claims for originality, for a new wave of Christian theology which would blow the lid off everything we thought we knew, turned out, then, to be little more than a limping through common ground that, at its freshest, grazed the 1960s, but mostly kept itself safely with centuries-old wisdom firmly restated with all the long-observed warts still manifestly in place.  A decided letdown.

Culture Music Science and Math

Humans are Great 5: Mathematicians and their Music

I was chatting with a Ukrainian friend the other day when she asked me, “Do you play any musical instruments?”  I admitted that I could, by certain not terribly high standards, be called a piano player.  “A-ha!  I knew it.  Math people are always music people,” she responded triumphantly, and started to list off all the people she knew who had a combined love of math and classical music.

Of course, we in the United States are bound to take all utterances from Ukrainians on the subjects of music, math, and ballet as unquestionably true.  But there’s a lot of supplementary evidence as well, from great mathematicians and physicists who either played an instrument or had a deep and profound love of music, to the necessary connections between what is great about math and what is great about music that attract one and the same mind.



It’s the structural similarities that get me.  Mathematics is the art of saying a universe while bound by formalist fetters of the toughest stuff.  Every word, every turn, has to bear the scrutiny of an epoch of rigor.  When you find something new to say within those confines, you’ve pulled off an unparalleled act of creation.  A stunning proof can get me positively teary-eyed, and it’s that exact same structure of finding creativity in the face of impossible restriction that touches me in classical music.

I’m going to take an extreme example because, hey, it’s the Holidays.  Consider the last movement of Beethoven’s Appassionata Sonata.  It is from his stormy middle period and is often used in film when they need a piece of piano literature for an unhinged virtuosic criminal mastermind to thrash out in the solitude of his mountain fortress.  Or maybe I just feel like it should be.  In any case, the restrictions are profound.  Leave out a note, and you’ve ruined it.  Ignore a dynamic marking, and you will be dropped from all men’s esteem.  Considering the freedom that you have as a pop star when covering a song to do pretty much whatever you damn well please as long as something like the melody of the chorus creeps through, it seems like there would be nothing left to individual human creativity when playing this piece of music.  We should have a hundred recordings, each a metronomical copy of the other, the only difference being the quality of the sound equipment employed.

And we do have a hundred recordings, but the amount of variation that the performers have squeezed out over the years within the constraints set by Beethoven is astounding.  Here is Wilhelm Kempff, one of the greats, performing it with his immaculate attention to the possibility for dynamic change within each measure (fast forward to 15:43 to get the third movement):


Now, compare that to Sviatoslav Richter’s performance, which basically conceives of the movement as an exercise in titanic thrash metal.  He is about speed and ferocity.  All the notes are the same, but the philosophical center of the piece is wildly different.



As I said, these are two extremes of an already extreme piece of music.  Part of the endless joy of classical music for my math-snuggling mind is sniffing out moments where performers do something unspeakably subtle that is entirely within the rules but that changes utterly the flavor of a piece, savoring that human ability to express individuality in the most seemingly unpromising situations.  Those moments have all the thrill of finding buried treasure, precisely because they are so hard to accomplish.  Further, once that new variation is discovered, it is added to our total experience of the piece, always there in the background, defining what comes after, so that each new performance is really a communication with all those that have come before.  Just as a mathematical proof is a conversation with Euler and Lagrange and Hilbert, so is each new Appassionata recording a piece of art that bears with it the decisions made by Kempff and Richter and thousands of others, and the more records you listen to, the better and richer each new record becomes.

So, get listening!

Books Comics Culture

The Lucifer In Us All

There is something deep within the structure of our ape-bequeathed brains that ever strains against the necessity of buying safety in the coin of freedom.  That call to mad, independent flight is the source of some of our greatest stories, and the characters who draw our rapt attention, generation upon generation.  And of those champions for pure freedom, none rings so elementally true as Lucifer, the angel who challenged his creator.


Of course, he failed, but the nobility of that failure, the humanity of it, have made him impossible to forget.  And so, from Dante to Milton to Goethe, Lucifer stands at the center of the story, the horror of his realm and the degradation of his fall sparking our curiosity and respect in ways that the subsequent, party-line marshaling of Heaven’s glories have never quite balanced.   We read Inferno out of a desire to understand our true stars.  We read Paradiso largely out of obligation.




At its best, fiction centering on Lucifer brings us to foundational grips with the tension between the lip service we pay to our love of freedom and our more commonplace (but civilization-building) need for things to be in proper and expected order when we wake in the morning.


At its worst, it is titillation mongering, and I admit I’m largely okay with that too.


But we are here to discuss an instance of the former case.  This year, Vertigo Comics has begun its long-awaited re-release of Mike Carey and Peter Gross’s Lucifer, which ran for seventy five issues from 2000 to 2006.  The first two books cover issues one through twenty-eight, with a third scheduled for release in March 2014.  I remember catching from issue fifty onwards when it first came out (which is saying something in light of my extreme Marvel partisanship at the time), but didn’t bother to hunt down the earlier trades until it was too late, so this was my first time laying eyes upon those first story arcs.


And they are exquisite.  Picking up where Neil Gaiman’s epochal Sandman left off, Lucifer has given up ruling Hell and runs a piano bar in Los Angeles from which he is turning over schemes to be free of Heaven and its determinacy at last.  That’s all you really need to know, and people coming to Lucifer without having read Sandman won’t be missing out on too much other than those “That guy we perceive dimly has some pretty spikey hair – I bet I know what that’s about” moments which are eventually made explicit anyway.


So, yes, you can come to Lucifer issue one, page one, with no continuity at your back and be well served.  Truth be told, Lucifer and Sandman are two very different beasts, the former an intense study of the character of rebellion and the philosophical thorniness of causality that is pure ambrosia to the likes of we humanist sorts while the latter allows itself to wander more broadly along the roads of its fancy, which is also exquisite but without the same rash, cocksure angularity that makes Lucifer so unique.  Lucifer Morningstar seeks one thing, and the comic is drawn along swiftly in the wake of that quest, and we as readers are hurtled briskly, breathlessly along, gasping to ourselves, “Can he?  Will he?  Should we be hopping off now, while it’s still safe?”


It’s precisely that vertigo-inducing sense of wishes fulfilled that perhaps oughtn’t be that I love so much about this comic.  Lucifer has the courage of his vision and the power to see it to its conclusion that we do not, as a day to day rule, share.  Nor should we.  Humanity would shake itself to pieces if our brains didn’t quell our Lucifer boldness in the oxytocin glow of community.  But thinking about where the boundary lies, between that need for permanence and the instinct to tear a hole in space and create our own kingdom in the void beyond, is the most important thing we can do, and Lucifer excels at ruminating on these issues.



I realize all of this focus on the book’s philosophy makes the comic sound perhaps like a ponderous slog through The Illustrated Heidegger.  But Carey is far too good a writer to let the philosophy ossify the story.  There are tales here of incredible scope and virtuosity – stories of demons turning to addiction in the absence of leadership, of the cards of fate inhabiting a cabaret performer, of a new Adam and Eve given the sole command to never bend their knee in worship of anything, of angels callously cutting a swath through innocence to maintain their hold on power, and of a dream walking girl having to fend off a creature armed with a thought-sucking straw.  It’s in every way marvelous, and Peter Gross’s art is perfectly matched to bring out the Baroque-modern harshness of Lucifer’s new plans for rebellion.


I suspect we’ll continue telling stories about Lucifer even after we have ceased being a religious species, because the point here is not religious.  It’s not about Christianity or the papacy or the rich absurdities of theology, though they all make their appearance.  It’s about the limits of existence, where they lie, and how close to them we dare tread.  And that will be of interest to humans so long as there are humans and, most likely, to whatever comes after us as well.

Art Culture

Humans are Great 4: The Agreeable Vice of Francois Boucher

There was a time, and perhaps after a century of Modernism Fatigue we are returning to it, when the business of serious art was, unabashedly, pleasure.  For a crisp but tenuous moment, delight ruled unencumbered by self-conscious moralizing or the strictures of reality.  If you could dream it, and it was charming, you painted it.  The era lasted all of about thirty years, born in the first flush of the Enlightenment’s love of sloppily amorous humanity, and was snuffed before its time by that same movement’s increasing need for classical and uplifting overtones in its artistic productions.  But, if you’re of a mind to sit dreamily drunk before a bit of art for a while, you’ll find a welcoming home there.


The high priest of the Pleasure in Painting was the Parisian artist François Boucher (1703-1770).  He came of age as an artist in that era when society, worn out by the somber realities of the end of Louis XIV’s reign, sought to recapture itself in the vigorous pursuit of life.  Part of that endless quest included the construction of ravishing private spaces bedecked with charming and graceful illustrations.  Boucher, their iconographer of choice, delivered a constant stream of pastoral simplicity, luscious nudes, and oh so very much drapery.


After spending his student years wrapped up in the obligatory production of obscure Biblical moments, Boucher broke into his own style by wedding mythological themes to a visual sense that combined Flemish and modern Italian influences with his own innate feel for dramatic elegance.  There is a lot of loveliness to contemplate from his first decade and a half, but this, his Birth of Venus (1740), is perhaps the most wonderfully over-the-top love song to the marriage of art and pleasure:


The Birth of Venus, 1740.



In the mid 1740s a pastoral fad broke out, and Boucher responded with a series of hyper-idealized but entirely fetching canvases that still have the power to make us stop dead in our twitchy, nervous tracks and melt a bit with a yearning for something slower:

Shepherd Piping to a Shepherdess, 1744.

Even those who hated him couldn’t help but admit that they kinda liked him.  In his famous attempt to wean the Parisian public from Boucher’s paintings and redirect its enthusiasm to more elevated artistic ground, Denis Diderot ended up basically advertising for him:  “What colors!  What variety!  What richness of objects and ideas!… There is no part of his compositions which, separated from the others, does not please you; the ensemble even seduces you.  That man has everything except truth…  Where has one actually seen shepherds dressed with such elegance and luxury? …. [but] one cannot leave the picture.  It fixes you.  One comes back to it.  It is such an agreeable vice!”


The Setting of the Sun, 1752.


For better or worse, ours is a time of agreeable vices.  We have all spent more on novelty tee-shirts depicting Daleks or Jayne Hats or Fluttershy Battling Medusa than on sober art-school originals because we think that amusement is the ideal wadding with which to stuff the gaps of life, even (or perhaps especially) as they yawn gradually into chasms.  I certainly have, and I don’t feel any particular shame on that account.  Agreeable vices are important, and deserve to be reckoned as such rather than cast off as unworthy of an artist’s labor.


I cannot deny, however, that, as much smack as I talk, I do love the callous challenge of modernism, indeed anything that sets out to make you do some work for your squirt of dopamine, but I am truly thankful that there was that rolling ripple of a time when artists were willing to indulge their fancy at the cost of their bottom-line profundity, and to let visual poetic discourse run where it would without philosophical theory dictating a curfew.

Culture Science and Math

The Disappearing American Science Student

Don’t they teach recreational mathematics anymore?!” – Doctor Who


No, Doctor, they don’t.  At least not according to Harold Levy’s sobering article in the new (Dec 13) issue of Scientific American, which rolls out some truly dispiriting statistics about the state of science and math enthusiasm in the United States.  For example, we learn that, in 2001, 65 percent of all electrical engineering doctorates awarded in the United States were given to foreign students, and that in 2009 46 percent of all master’s degrees in computer science went to students on foreign visas.


And no, the phenomenon has nothing to do with Diversity Quotas, so you can put that speech away, and everything to do with our inability to produce inspired and inspiring first-tier college students out of our high school system.  As a calculus and physics teacher since 2003, parent since 2004, and private tutor since my high school days, I’ve been watching this trend, first-hand, from a few different angles.  The good news is that the educational community is by no means taking these trends lying down, and some very exciting things are in the works which stand to make us a much more scientifically literate nation.


One of the things that I, and many math-first people of my ilk, have done much wrong-headed grumbling about is the rise of the Conceptual Science curriculum.  It started with physics, is making its way into chemistry, and is basically an attempt to give people solid scientific instincts independent of advanced mathematical skills.  Originally, the idea was that these Conceptual classes would be a good place to stuff struggling students, so as to cut some of the dead weight from the normal and honors physics classes.


Which led to unfortunate things, because the teachers that were stuck with the Conceptual classes tended to be on the bottom of the seniority poll, and so you had rookies teaching castoffs which, in spite of what the movies say, ends rather more often in disaster than inspiration.  But then people started realizing the raw potential here.  To illustrate, consider the following two problems, the first a typical physics class question, and the second a typical Conceptual physics question:


  1.  Two forces act on a 4 kg rope in opposite directions, one of magnitude 300 Newtons, and the other of magnitude 500 N.  Calculate the Tension in the Rope and the acceleration of the system.


  1. Two guys engage in a game of tug-of-war.  If they both pull with 200 N of force, what’s the tension in the rope?  Now, what would the tension be if we replaced one of the guys with a tree?


The first invites the student to construct a free body diagram, derive the relevant Newtonian equations, and solve for some desired variables.  All very standard and expected.  The second asks you to think, really think, about just what is going on here.  DOES it matter if I replace a man pulling backwards with a stationary tree?  Shouldn’t it?  But maybe not… why?


I try to incorporate these moments whenever I can into my AP Physics class, to break the students out of their very meticulously learned algorithms, and make them think about the actual physicality of what’s going on, to develop sure scientific instincts about what matters and what doesn’t, to get them debating about the variables and how they come into play.  It’s that intuition that my parents’ generation had but that, swamped with the need to perform well on standardized tests, was systematically murdered by the educational system over the course of several decades.  It is recreational- you are playing and weighing and arguing and having a grand old time talking about a rope and a tree, which is precisely the sort of free intellectual play that sustains people in their interest to pursue the rigorous course of a scientific education.


So, that’s all great, and it’s getting injected more and more into all levels of the high school curriculum.  But it’s not quite enough.  It’s not enough to just think about science and math until the end of your assigned problem set.  We need kids who actively choose to spend their leisure investigating problems that they find interesting, delving more deeply into topics they find compelling.  And that is all about parental modeling – the kiddos need to see from their earliest days that, the work day done, their parents don’t just flop insensibly into the warm and easy embrace of television, booze, or incessant Facebook nattering.


They need to see parents with intellectual hobbies, really ANY intellectual hobbies – a dad who takes a half an hour each night to read through some poetry, not because it broadens his education, but because he actually enjoys it.  A mother who has a few Erlenmeyer flasks in the garage for an experiment now and again.  Something that shows the kids that the care of one’s mind can actually be a joy far surpassing mere satiation.  They take their lessons in the use of recreational time from us – in many ways it’s the most important thing we have to teach them, and the one easiest to neglect.


But.  If we do make a sort of civilizational commitment to being mindful of our leisure hours, and if we do continue to find ways to structure curriculum to spark surprise and argument instead of the comparative ease of an expected algorithm, we have a chance to raise a remarkable generation of thinkers.

Culture Language Music

Humans are Great 3: Falco’s Music Videos

There comes a moment for us all, our work being done, our chores accomplished and living nook tidied, when we have no choice but to pull up a chair opposite cold, dour Reality and evaluate the content of our lives.  It is the easiest thing in the world, in that moment, to either lock one’s self into an iron stoicism or simply despair at the futility of it all.  My respect has always gone, however, to those who see a third way out of the grim facts of existence, who fully recognize the insistent press of entropy and yet manage, through a pure genius for goofiness, to make life a little more radiant for the rest of us.  When I think about my favorite bits of humanity, unabashed goofs spring to mind far more often than po-faced anguish-mongers.  And the crown prince of the ridiculous is, without a doubt, 80s German pop music sensation, Falco.

If that name rings a bell at all, it is because you are over 30 and remember this, the video to Rock Me Amadeus, which features Falco in an elegant tuxedo rapping in German about Mozart while walking through a crowd of punk aristocrats and motorcycle gangs.   It connects, through two centuries of European history, the madcap genius of Mozart with the living silliness of the 1980s in a way that you can’t help but be enchanted by if you have an enchantable bone in your body (the video proper begins at 0:27):

Wonderful.  Really, though, the wackiness here is understated in the general canon of Falco videos.  Take my personal favorite, Wiener Blut, which features Falco, dressed alternately as Napoleon Bonaparte and a fish-tie wearing corrupt politician, mixing in with an incongruous selection of overweight German tourists, mafiosos, Flashdancing female police officers, and I’m not quite sure what all else:

Or The Sound of Musik, Falco’s ode to the development of music itself, which begins with Falco as Mad King Ludwig of Bavaria rising up from a silk-strewn floor and then explodes into a just joyful celebration of our love for sound.  Every moment of it is absolutely ridiculous and absolutely beautiful.  You can’t watch it and not think, “You know, humanity’s all right.”

Falco is entirely aware of our capacity for darkness, and some of the more over-done aspects of even his most effervescent videos key into those dark zones.  Lest we forget, his second big hit, Jeanny, is a song explicitly about child kidnapping, and the video is about as dark as you can get:

But it’s the existence of videos like that which makes Amadeus and Wiener Blut so much more delightful.  They sizzle with an awareness of our great capacity for self-harm and the determination to overcome all of that in a great orgiastic celebration of our common bond.  Be you a grotesque tourist, a biker, or a man with a gauge for a head, there is a place for you at Falco’s table of humanity.  If, as humanists, we could tap into this vein a bit more and into our valuable but rather mopey instincts for phrase parsing a bit less, it might do us, and those people proximal to us, a decided good.

Books Culture

Jedi or Trekkie? The Humanist Perspective




The [Jedi] Order has long been about justifying its own existence, about acquiring and holding power… I know what I swore to do as a Jedi, and it didn’t have anything to do with turning a blind eye to social evils because the Sith were a bigger evil.  – Gotab (Bardan Jusik)




Your report describes how rational these people are. Millennia ago, they abandoned their belief in the supernatural. Now you are asking me to sabotage that achievement, to send them back into the Dark Ages of superstition and ignorance and fear. No!

– Captain Jean Luc Picard



Ask any sensible 25 year old human which they prefer, Star Wars or Star Trek and, without missing a beat, they will reply Star Wars and proceed down the list of its clear advantages.  It’s more exciting.  There’s more action.  The bad guys are cooler.  It’s grittier.  It has women in leadership positions before 1990.  The aliens aren’t just people with face paint.  There’s magic.  Light sabers, dude, light sabers.

And so forth.

Ask any 35 year old, and the answer just as inevitably comes back Star Trek, and especially from the people who most vociferously insisted Star Wars a decade prior.  It’s about bigger social issues.  It’s philosophically more subtle.  The science is more interesting.  The team dynamic is more compelling than the series of lone wolves that Star Wars has to offer.

And so on.

The implication seems to be that Star Wars is the stuff of idealistic, solipsistic adolescence, and Star Trek that of pragmatic, socially-oriented adulthood, but that is to do a disservice to the philosophies of power and social change present especially in the Star Wars expanded universe, and the sense of individual struggle to be found in Star Trek’s most recent instantiation.

Starting with Star Wars, I won’t attempt to instill the original films with more philosophical weight than they had.  The movies were the defining experience of my childhood, and merchandise related to them continues to consume more of my personal income than I care to reveal.  They are thoroughly rad, but they aren’t particularly deep.  They do, however, contain themes of astounding pregnancy which have been worked by others into fascinating ruminations about how change happens in civilization.

The best place to go to find this broader scope is undoubtedly the novels, of which there are hundreds, but the high point for me is definitely the nine-novel Legacy of the Force series, and particularly book eight, Revelation, by veteran Star Wars novelist Karen Traviss.  The series centers upon the rise of Jacen Solo, son of Leia and Han, who possesses force abilities of untold power and flexibility, and seeks to use them in the service of a galaxy just rebuilding itself after disastrous invasion.  It is hardly worth the hauling out of a Spoiler Alert placard to say that the Dark Side soon has him in its clutches.  But what’s interesting is that the Dark Side isn’t some metaphysical notion of pure evil, but rather a philosophy about how you institute reform in a civilization.  Presented with the self-serving inertia of those in power and comfort, how do you make life better for those actively but voicelessly suffering?

In grappling with this issue, the Legacy books are really looking at the structural flaws of Buddhist versus Christian practice.  The Jedi, whose espousal of detachment allows flagrant injustice to continue in the galaxy so long as their precious monastery stays in power, are everything that’s wrong with a classical Buddhist approach to society, and Jacen soon grows frustrated with their mysticism-laced unwillingness to get their hands dirty to help people.  The Sith, full of absolute confidence in the righteousness of their own actions, gifted with the ability to take action in the name of galaxy-spanning goals regardless of consequence, are the Christians, drunk on their own supernatural power and convinced that anybody who opposes them opposes the universal order and therefore deserves death.



Jacen is tossed about on the horns of these polarities until the sheer need for resolute action in order to save the galaxy tosses him into the arms of the Dark Side.  During one of his moments of introspection, he basically rewrites the original trilogy, showing that the Rebellion, in acting as it did, was far more Sith than Jedi in affiliation:

“Who would make the tough choices if they were hidebound by conventional law?  Had anyone protested about Luke Skywalker bringing down Palpatine?  The Rebellion broke every law in the book, and killed many people, but citizens were ready to accept that because change was needed.  [Jacen] was only doing the same thing, and yet he was vilified for it.  He was wounded by the blindness around him.  Why could they not understand?  He wasn’t explaining it clearly enough, perhaps.”

Ultimately, the fallout from all of this propels the Star Wars universe into The Fate of the Jedi series, which finds the Jedi in disgrace and the galaxy questioning whether or not we’d be better off after all without these self-appointed paladins of disinterested virtue in charge.  These books make the original movies retroactively more profound, and are worth the reading by anybody wanting to expand their love of a galaxy far, far away into that stage of life that needs something more than the hiss of a light saber to capture its interest.


To Star Trek, then, and particularly to the most recent series, Star Trek: Enterprise.  Responding to criticism that The Next Generation, Deep Space Nine, and Voyager were essentially tales of space bureaucracy incapable of bringing in a younger audience, Enterprise went back to the very beginning of humanity’s interstellar program to catch us at a moment of cocky inexperience, before the Prime Directive, before the diplomatic concerns of negotiating borders with the Romulans.  The crew, led by Captain Jonathan Archer, manifestly does not know what it is doing half the time, and in the space that protocol usually fills, they are left to suss things out for themselves as best they can.

And in that sense, this series is much closer to Star Wars than to the previous offerings of Star Trek.  It is consistently about individual agency and power, and how that ought to be used to accomplish what you find to be the right task, precedent be damned.  Whereas an episode of Voyager (incidentally, my favorite of the Trek series, though I realize I’m basically alone in that) will feature the crew agonizing over the application of Federation protocol to a particular instance, in Enterprise the issue Archer is constantly facing is what his power as a starship captain morally allows him to do, and what it compels him to do, which is a very Jedi/Sith kind of dilemma.

The framework, however, is still very Star Trek, in that Kantian philosophy and enlightened skepticism come to the rescue more often than not.  The categorical imperative is the big machine that dictates how the episodes are going to turn out, while appeals to mystical explanations and vague religiosity, which cropped up from time to time in Voyager, are routinely squashed in favor of freedom of thought and the scientific method.  It is entirely an amalgam of the personal drama of Star Wars and the larger concerns of Star Trek, with the occasional manifestly gratuitous Decontamination Room Scene by way of fan service.


The title of this essay implied a solution, that the weight of judgment would settle finally on one pole or the other of this, the most important question of our times.  Certainly, looking at it casually, a humanist would be better rewarded investing their leisure hours in old Star Trek episodes than in repeat viewings of Star Wars, but that is to undervalue the richness of Lucas’s original conception, one which set the stage for big questions to be asked, even if he didn’t himself ask them.  There is no need to hang up your Mandalorian armor upon reaching the august age of 30.  Nor must you seek islands far from the Trek universe if you want to probe issues of individual psychology.  The answer to Trekkie or Jedi is, simply, BOTH, or if you have utterly no sense of imaginative play, then NEITHER, but to alight on one side or the other exclusively is to do yourself a profound disservice.

Now, Marvel or DC, on the other hand…. That one’s easy.

Science and Math

Humans Are Great 2: The Popcorn Function

Mathematics is the summit of everything I find wonderful about mankind.  It requires the most rigorous thinking of which we are capable married to an unflinching creativity, astounding sense of space and movement, and a poetic regard for the pregnancy of words.  Technically, I suppose that’s a marriage on the polygamous side, but I’m all for that too.  In any case, once you get past the decade-long tutorial, learning the names and rules for all the different tools, you get to start having fun trying to Break Math.  Seeing mathematicians hot on the hunt for something that will tear down a millennia-long assumption is really quite beautiful, and another example of humans just being great.

One of my favorite examples of Math Gone Mad is called (among other less whimsical names) the Popcorn Function.  It goes like this:


F(x) = { 1/q if x is a rational number of the form p/q.

0 if x is irrational. }


And here is a snapshot of a part of it.


The Popcorn Function!


It’s popularly called the popcorn function because all of the rational x’s pop up to one over their denominator, while all of the irrationals stay stuck on the x-axis.  Now, think back to your high school Pre-Calculus or Calculus class.  You might remember a working definition of continuity that says, “A graph is continuous if you don’t have to lift your pencil while drawing it.”  Just looking at this picture, it is hard to picture something LESS continuous-seeming.

AND YET, it turns out that this function is continuous at all irrational numbers but discontinuous at all rational numbers.

That seems a rather wildly improbable statement, and yet the proof of it is delightfully uncomplicated, and in fact is something you might want to whip out at your next cocktail party while the Catan board is getting set up.  It all relies on a more rigorous definition of continuity, known as the ε-δ definition.  Just written out, it looks horrid:


“A function f(x) is continuous at x=a if, for any ε > 0, there exists a δ > 0 such that if |x-a| < δ, then |f(x) – f(a) | < ε.”


When I introduce this to my calculus students, there is usually a fair amount of rending of clothing and gnashing of teeth, but the idea is actually very simple: “If two x values, let’s say a and b, are close to each other, then f(a) and f(b) should be close to each other too.”  It’s the pencil requirement written mathematically – to move right a little bit while drawing my curve I shouldn’t have to move up or down very far.

So, to prove that something is continuous, I have to show that, for any value of epsilon (ε), no matter how small, I can find a neighborhood of x values around x=a that all end up within ε of f(a).  Alternately, to prove that a function is NOT continuous at x=a I just need to produce a value of ε for which it is impossible to find such a neighborhood around x=a.

Now, I said that the Popcorn Function is continuous at every irrational number and discontinuous at every rational number.  Let’s start with the easy part, proving that the rationals are discontinuous.  To do it, I’m going to use a smashing attribute of the number line – that the irrationals and rationals are “dense.”  That means that, no matter how small a step I take from a rational number, I’m going to cross infinitely many irrationals, and no matter how small a step I take from an irrational number, I’m going to cross an infinite number of rational numbers along the way.  Any neighborhood, no matter how small, of any number will contain infinitely many other irrational and rational numbers.  There is just as much richness to contemplate from 0 to 1 as from negative infinity to positive infinity.

So, let’s say that my “a” value is rational, so f(a) = 1/a.  I’m going to choose 1/2a as my ε value.  Now, no matter what value of delta I choose, there are going to be infinitely many irrational x-values within that neighborhood of a, all with a function value of 0.  So, |f(x)-f(a)| for those irrational x’s will equal 1/a, which is more than our ε value.  So, not all points within any delta of a will end up within ε of f(a), so the function is not continuous at x=a if a is rational.  Neat!

But we have barely begun to climb Mt. Nifty.  Now, suppose a is irrational (so, f(a) = 0), and that I choose some random, rational value for ε (if the fact that I’m limiting ε to rational numbers disturbs you, good, but if you really want to use an irrational ε, I can always find a rational one both smaller than it but still positive, and use that ε for the proof).  Epsilon, being rational, has an integer denominator, let’s call it q.  So, all I need to do is find a delta neighborhood around “a” that definitely does not contain any x values with a denominator smaller than q.

And, it turns out, I can do that.  Think about it.  Let’s say my “a” is equal to 2 point something something something.  Now, between 2 and 3 there is only one reduced fraction with denominator equal to 2 (namely, 5/2), only 2 with denominator equal to 3 (7/3 and 8/3), only 2 with denominator equal to 4 (9/4, and 11/4), and so on.  The point being, that no matter how big q (the denominator of my original ε) is, there are only a finite number of rational values around a with a smaller denominator.  Since there are only finitely many, one of them will be CLOSEST to “a”.  If I choose my delta just smaller than that distance, I am absolutely guaranteed that no x value within that delta neighborhood will have a denominator smaller than q, and as such, f(x) will always be less than ε, and so, at x=a, the function is continuous!!

And one more ! for good measure.

So, in spite of the fact that there are infinitely many places where this function is hopping up off the number line, it is actually, technically, continuous at every single irrational number.  What’s even weirder is that, and here I’m going to turn to the calculus-remembering folk for a bit, this function is actually integrable too, since its set of discontinuities, the rational numbers, is countable!  *Electric Air Guitar Riff!*

Wrapped up in this one function is a large part of all my favorite stuff about math and about the humans who make it.  There are some spectacularly clean definitions that have been seized upon by some wonderfully playful minds to create an object that breaks every bond of common sense.  It’s the same process or rules-brokered explosive creativity you see in Beethoven’s Third Symphony, or the perspective tinkering of a Braque canvas, only rendered, at least for me, several orders of magnitude more exciting by virtue of being so ethereal, so elusively abstract.

It’s like I always say: If you love poetry, you’ll love math more.  Eventually.


FURTHER READING: If you liked that function, there are tons of other such to be had out there.  A great place to start is Bernard Gelbaum and John Olmsted’s Counterexamples in Analysis, which is a book of nothing but dastardly clever things that seem to defy common sense.  To get most of it, though, requires something of a background in Real Analysis, for which Charles Pugh’s Real Mathematical Analysis is a great starting point that just about anybody can dive into right away!