On a Tangent


You might be thinking, what is that?  And what does it have to do with me?  Or maybe you’re just thinking: Gosh, that looks beautiful – I wish I knew how to make such pretty pictures.

For the latter sort, you could get a math degree, or you could take a shortcut and read my tutoring blog, where I explain other marvels and will soon get into some more technical detail about today’s work of art.  But for the former, read on.

We start off with some really weird curve (read: I mashed a few keys in a graphing program and worked with what came up).  Now, if you were an ant on there looking close up, how would you visualize that curve?


Maybe you’d think that it was just a line, a line heading off at that same angle that you currently find yourself.  Maybe, as you walk along, you’d constantly revise your view of the world:


Such an ant could manage themselves just fine.  As long as they keep looking at where they are, they can make it around the curve.  But their conception of the world at large is completely off.  Almost every single judgement they would make about other points on the curve would be wrong.  The ant can live in the “now” as long as they keep it to themselves.

But our ant could be a little more sophisticated:


This second ant is still using data merely from their local environment; they just estimate a curve of best fit, instead of a line (in mathese: they find a tangent conic, instead of a tangent line.  In worse mathese: they use a truncated Taylor series as calculated at that point, the general technique for all estimations in this post).  This curve still doesn’t match the overall pattern very well, but it does a darn sight better at making decisions about the neighbourhood.

A third ant might be a little more resourceful, and come up with this:


Or this:


Now, this ant can start making broader claims about the world.  The ant will still be off, but significantly less so than the previous two.  And finally, we have genius ant here:


Again, this ant’s knowledge is not perfect – but she absolutely nails entire portions of the world, using just the information that is at her immediate fingertips.  She doesn’t have a larger view of the world, she has a deeper view.  Maybe she still lives in the “here and now”, but she doesn’t rest content with mere appearances.  She doesn’t just calculate how things are, or how they are changing, but how change changes, and so on (technically, up to 8th derivatives).  By assuming that everything is changing, including change itself, she can understand.

And as a bonus (which I’m not sure has any analogical value, but which looks cool), here’s all of the approximations together in one animation:



Arbitrariness and Meaning

Why drive on the right side of the road?  The left works for the Brits.  Why start question-words with wh- instead of k-, as does Sanskrit, Farsi, and certain dialects of Ancient Greek?  Why read left to right?  We could go right-to-left, like Hebrew and Arabic, or even top-to-bottom as is sometimes done with Chinese.  Why is i the square root of -1, when (-i)² also equals -1?  Why does a clock go clockwise, when making it go anti-clockwise would work just as well?

All of these choices are purely arbitrary.  The alternatives would have worked equally well.  But refusing to choose one between equivalent choices would have left confusion; it would have erased the possibility of meaning and cohesion.

Meaning starts from the meaningless; from de-cision, that is, cutting something away.

The paradox of “Buridan’s ass” is about a donkey that is faced with two equal succulent bales of hay, both the same distance away.  Does the donkey starve since there is no reason to choose one bale over the other?  Al-Ghazali similarly writes,

Suppose two similar dates in front of a man, who has a strong desire for them but who is unable to take them both. Surely he will take one of them, through a quality in him, the nature of which is to differentiate between two similar things.

So the rational rests on the irrational; because without this symmetry-breaking, nothing happens.

Emotional Robots

Picture Data from Star Trek.  The quintessential robot: all reason and logic, no emotion.  Not that he’s heartless, but rather, he just doesn’t understand this side of human behaviour, no matter how hard he tries.  (Except when it makes for a better plot point otherwise.)

But what are emotions, other than our own preprogramming?  Those who are at the mercy of the passions are the ones blindly following their hardwiring.  Those who can’t take a step back and look at why they really are doing what they do, those who are wounded by the suggestion that we are organic machines with modules shaped by our biological and sociological histories, are those who end up being the most robotic.  Machines running on chemicals masked as “spirituality” and “humanity.”  It is at our most irrational that we are most programmed.

Even the cold logic of economists and engineers follows the same route: a search for logical efficiency and consistency, but stuck in the rut of an initial question that is not itself questioned.  The precision of gears, working toward an initial impulse to categorize, simplify, and control.  The dominance of their evolutionary firmware is less apparent, but ultimately the same.

Being human is neither revelling in feeling for its own sake, nor in mere logical analysis (which is much the same); rather, it consists in the ability to look behind the curtain at who we are and where we come from, to understand, to make decisions based on this; it is to be able to make sense of our own owner’s manuals and fiddle, reprogram, rewire, and, in the end, simply accept what sort of beings we are.

Because we are, after all, organic machines.  Our emotional operating systems are part of us, and must be taken as such; just as a computer cannot run without some sort of system to boot it up and manage resources, so too must we rely on our own frameworks, imperfect as they may be.

But we don’t worship Windows because we have to use it. Valorization of the emotions as distinctly “human” or as some royal road into reality is similarly misplaced.

The Re-enchantment of Reality

Logic.  Analysis.  Criticism.  Sometimes, the only function of these seems to be to remove any sort of mystery or wonder from the world.

And this often is, unfortunately, a first step.  We do have do give up cherished beliefs.  But there is no need to stop there.

This disenchantment is merely a removal of our false enchantments.  As long as we cling to our quick cures, love-lorn logics, senses of soul, and desperate desire for immortality, as long as we stay in the sandbox with our simple magic spells, we miss a larger world around us.

The message of science and rationalism is not that there is no fairy tale.  It is that human beings are not the centre of the tale.  The dragon did not abduct our princess and the fey are unconcerned with our children.  Magic only sees the marvels that are manipulated for ourselves.  Science lets us look at wonders for their own sake, and so reveals so much more than the magical imagination could dream of.

We live in a world teeming with life, including single-celled organisms, massive creatures both past and present, things that strain any definitional limit we would place on life, and beings inhabiting the oddest and most inhospitable portions of the globe.  Evolution may be as blind and clumsy as Cupid, but look at the mysterious world slowly shaped and moulded from such simple principles, created a unified family history of life binding us all together. 

The utterly incomprehensible distances of the Universe, the massive furnaces which produce both all of our energy and our matter, spots of mass so dense that they literally bend space and time to their whim – these team with bizarre particle-waves defying all attempt at common-sense description in forming the entire world around us.

And that is merely the briefest of beginnings.  Leave your imaginaries behind – not because they are fantastic, but because they are not fantastic enough.  Following our initial desires and perceptions, we form security blankets for ourselves, comforting but devoid of aesthetic value.  Critical, close observation lets us see the stories going on all around us.