A man stands clad in chrome and gold
And goes to war with ink and verse,
Lest history remain untold

With blackened eyes and heart accursed,
His foe is censored doom and spite
And goes to war with ink and verse—

The verse perverse, redacted blight
Entombs in sable pools his home
His foe is censored doom and spite

Two swift swords flash, red-splattered chrome
A child turns around to flee
Entombed in sable pools his home

A broken mouth coughs out the plea:
Take up your sword, your past recall
A child turns around to flee.

The sun will rise, the sun will fall
A son stands clad in chrome and gold.
Take up your sword, your past recall
Lest history remain untold.

Personal Dictionaries

One of my favorite features on my smartphone — and this is on a device that gives me unlimited access to YouTube, Wikipedia, and a Gameboy Advance emulator, so that’s saying something — is my personal dictionary.  As I use the phone, I add words that I use commonly to this digital repository of my own personal vernacular, and it’s always a kick to read through it and see what I’ve been talking about.  The dictionary usually ends up being a mix of the profane, the really profane, the incredibly profane, and some uncommon first names.

It’s also wiped every time I get a new phone, which is a shame, since I’ve glided through a few different argots since entering the smartphone age: college, grad school, real world.  For posterity’s sake, I think I’m going to make a conscious effort to track this dictionary from now on, so I have a record of what was (linguistically) important to me over two-year, phone-contract-length periods of my life.

Here’s where I’m at on my current phone, purchased July 2014:


There’s something magical, in the Arthur C. Clarke sense of the word, about compression algorithms — take something that’s too big for a box, and squeeze it into that box regardless.

But, of course, not everything can simply be squeezed smaller.  Some coworkers and I were talking this week about needing to extract the information in an image from a range of wavelengths about a nanometer wide, and how that wouldn’t really just work by filtering an optical image repeatedly (the range of light visible to humans is about 300 nm).  Encoding enough information in the original image so that filtering it down is actually useful — and so that the original image doesn’t take up a server farm worth of digital storage — would probably take a huge amount of compression, ratios of 1000 or 10,000 to 1.  To put that in a little bit of perspective, an uncompressed song file would be maybe 50 MB, while an .mp3 of the same song could be as little as 3.5 MB — a 14:1 ratio.  So thousands-to-one is a lot.

This is when one of the PhDs who started this conversation compared this task to trying to represent The Iliad as a limerick.

Well, challenge accepted.

It varies by translation, but The Iliad is about 150,000 words long.  A limerick, in its classic form, is two lines of two anapests (those are the ones that go “da-da-DUM”) sandwiched between three lines of three anapests for a total of 39 syllables.  It was surprisingly hard to find a good answer for the average number of syllables in an English word, but 1.3 seems to be a good guess.  (If you’re interested, you can look at this paper or use this online calculator, which I dropped some public domain works into: The Time Machine, Huckleberry Finn, and The Picture of Dorian Gray.  You can also look at this Wikipedia list, which is mostly unrelated but fantastic.)  That means 39 syllables is approximately 30 words, and turning Homer’s epic poem into a form more widely know for New Englander autofellatio jokes is about a 5000:1 compression — an impressively accurate off-the-cuff analogy for what we were talking about.

Here’s my shot at The Iliad in limerick form:

With abduction of Helen the source,
Menelaus responded with force
So the Greeks sailed for Troy
Set to burn and destroy
But just eked out a win with a horse

And why stop there?

How about the Old Testament in haiku, or taking 600,000 words down to 17 syllables (13 words-ish)?

Birth of light, then man
Wandered until given rules:
Be nice, no bacon

I’m open to suggestions for future compression here.  Will update this post as I have more ideas.

They See Me Rollin’

Whenever I talk about math in this blog, you know it’s going to be something that is simultaneously incredibly important and incredibly useless.  Today is no exception — I want to tackle one of the most important (but no worries, also useless) examples of polar coordinates and path-length integrals around, even if you don’t realize it yet:

When you have a roll of stuff — think paper towels, aluminum foil, Saran wrap, use your imagination — how much of that stuff is left, based on the diameter of the roll?  How many more chicken dinners can you cover and stick in the fridge?  How many more spilled beers can you wipe off of the table?

(This question, for the record, came up at work, albeit with some industrial polymer examples instead of household chores.  The times I do real math as a mechanical engineer are surprisingly few and far between, so apologies if I come off as over-excited.)

On one level, this question isn’t that tricky. Your roll of stuff — I’ll stick with aluminum foil in these examples — is wound around a core, and you can measure the core diameter, measure the roll diameter, measure the thickness of the foil and chug-chug-chug along until a number comes out.

Which is, of course, exactly what we’re going to do first.  (Spoiler alert: there’s a massive shortcut and a cool arithmetic trick at the end, but we’re going to slog through some calculus because I learned all this shit and never get to use it, goddammit.)

The foil is wound around the core in a spiral — an Archimedean spiral, to be precise.  Each layer sits directly on top of the last layer, around and around and around, until it reaches the point you pull.

In polar coordinates, the equation for an Archimedean spiral is r = cθ.  (Polar coordinate recap: angle, θ, and distance from the origin, r, are just as valid a way to define a point’s location as x and y, and the bears are white instead of brown.)  The constant c defines how much space is between each turn of the spiral; in our case this is directly related to the thickness of the foil, which I’ll call t.  Every winding around the core, a distance of 2π radians, increase the roll’s radius by t, so we have:

c = t / (2π)

Therefore the equation of our aluminum foil spiral is:

r = tθ / (2π)

Without deriving it here (I let Stephen derive it here instead), the length of a curve — any curve — in polar coordinates is given by:

Screen Shot 2015-01-29 at 9.12.38 PM

Our starting and ending coordinates, θ0 and θ1, are given by the radius of the core the foil is wound around (r0) and the outer radius of the roll (r1), as well as our Archimedean spiral equation.  We get:

θ0 = 2πr0 / t

θ1 = 2πr1 / t

Putting this all together, we get:

Screen Shot 2015-01-29 at 9.13.56 PM

This is, uh, not a nice integral to solve.  But we’re really good at calculus (and by “we” I mean “Wolfram|Alpha”), and so we know this evaluates to:

Screen Shot 2015-01-29 at 9.15.15 PM

Holy dammit Christmas, we’ve gone hyperbolic.  If it makes you feel better, we can write the inverse sinh function as a logarithm, and so this soup of advanced math classes reduces down to:

Screen Shot 2015-01-29 at 9.15.58 PM

Okay, fine, it’s still not pretty.  But it is precise.

Standard household aluminum foil is about 0.016 mm thick.  If it’s wrapped around a 12 mm radius core to a final outer radius of 16 mm, this formula tells us that it should have a total overall length of 21.99 m — enough for a whole lot of Chipotle burrito swaddling, and just about exactly what we’d expect.  Two points calculus.

•    •  • • •  •    •

The engineer-graduate-degree half of my brain is done at this point (we have, after all, the most exact answer possible, though it took a decent amount of computation to get there).  But the undergraduate-physics-degree half of my brain, which was at one point instructed that pi is “approximately 1” and prides itself on Fermi estimation, doesn’t love all the work we had to go through to pull it off.  I mean — path integrals?  Hyperbolic trig functions?  Really?

What if we assume the foil is wound in concentric circles instead of a spiral?  This way simpler geometrically (ignore the fact that it’s physically impossible, please — this is a physics approximation after all), and since aluminum foil or paper towels or whatever are so thin the answer should be very similar.  In this case, the radius of each subsequent winding increases by exactly the thickness of the foil.

So if we add up the circumferences of all the concentric circles from the first to the Nth, we get the overall length of the foil:

s = 2πr0 + 2π(r0 + t) + 2π(r0 + 2t) + 2π(r0 + 3t) + … + 2π(r0 + (N – 1)t)

Or, rearranging:

s = 2π(r0 + r0 + tr0 + 2t + r0 + 3t + … + r0 + (N – 1)t)
s = 2π(Nr0 + (1 + 2 + 3 + … + (N – 1))t)

Lurking in here is a really neat arithmetic identity — the sum of every number between 1 and x (here, x is played by N – 1).  There’s an apocryphal story about a young Carl Friedrich Gauss, whose 18th century elementary school teacher tasked his class with summing every number from 1 to 100 — presumably to shut the little bastards up while the teacher nursed a massive Oktoberfest hangover.  While every other student began to assiduously add numbers up, our wunderkind Gauss thought about it and came up with a much more elegant solution: each pair of numbers — 1 and 100, 2 and 99, 3 and 98, etc. adds up to exactly the same value, and there are exactly 100/2 = 50 of those pairs.  Therefore the sum of all numbers from 1 to 100 is:

(100 / 2)(1 + 100) = 5050

That Gauss guy was a smart dude.  There’s a reason literally everything in mathematics is named after him (well, him and Euler).  In algebraic form, the sum of all numbers from 1 to x is:

(x / 2)(1 + x)

And for us, where x = N – 1:

(1 + 2 + 3 + … + (N – 1)) = ((N – 1)/2)(1 + (N – 1)) = (N2N) / 2

So that means the length of our roll is approximately:

s = 2π(Nr0 + ((N2 – N) / 2)t) = πN(2r0 + (N – 1)t)

We still need to figure out how many turns are in our foil coil, but that’s just based on the inner and outer radius:

N = (r1 – r0) / t

Putting everything together, we have:

s = π((r1 – r0) / t) (2r0 + (((r1 – r0) / t) – 1)t)

s = (π / t)(r12 – r02r0t – r1t)

Somehow this just looks much nicer than the solution with a hyperbolic trig function in it.  And when you plug the same numbers in, you get — wait for it — 21.98 m.  That’s a 0.01 m difference over more than 20 m of length… or a discrepancy of less than 0.05%.

So yeah, I’ll stick with Gauss on this one.  You can call it intelligence or you can call it indolence, but either way I know how many dinners I can wrap up and shove in the fridge.

NASAing of Teeth

Buckle up, boys and girls, because it’s three weeks into 2015 and I am already fucking livid.

I know that I’ve gone off before on science in politics — or, agonizingly predictably, lack thereof — but I have to do it one more time.  I have to, really, because we just put Ted Cruz in charge of NASA.

Okay, so not exactly in charge.  To be precise, the midterm election turnover in the Senate means Cruz now chairs the Subcommittee on Space, Science, and Competitiveness (Oxford comma officially omitted, but added here out of compunction), which oversees NASA, the NIST, the NSF, the OSTP, and apparently about 30% of all acronyms.

Why is this bad news?  By all accounts, Ted Cruz is a smart dude.  He was his high school valedictorian, went to Princeton and Harvard Law.  He should be the best of the best of what America can offer up, the upper crust of elite erudition that decides to apply itself to solving the country’s problems and propelling it into the next generation stronger, smarter, better than it was before.

Instead, Ted Cruz says shit like this:

My view of climate science is the same as that of many climate scientists.  We need a much better understanding of the climate before making policy choices that would impose substantial economic costs on our Nation.

Hi, Ted?  I have NASA on the line here.  You know, that science agency you’re about to be responsible for.  Lots of glasses and calculators and pocket protectors and weird-looking mohawks.  Anyway, they just wanted to make sure you’re aware that NINETY-FUCKING-SEVEN PERCENT OF ALL CLIMATE SCIENTISTS believe they have a handle on what’s going on, and that we need to do something about it.

Oh, but “[the] data are not supporting what the advocates are arguing”?  For a guy who knows how to use “data” correctly in a sentence, that’s not a very smart thing to say.  Here’s this thing we scientists like to call a “graph”:


So the truculent Ted Cruz, who is either so brilliant he knows something the rest of us don’t or so willfully ignorant he refuses to acknowledge something the rest of us see as self-evident, is going to watch over our nation’s science policy.  I feel about as comfortable with that as I do leaving my future children at Mikey Jackson’s Daycare Center and Used Needle Emporium.

I realize that it’s maybe unfair of me to extend Cruz’s views on climate change to the rest of his scientific thinking.  But I have to.  I have to, really, because you don’t trust heart surgery to someone who believes in the healing power of leeching.  You don’t trust bridge building to someone who doesn’t know a truss from a trull.  You don’t trust polymer science to someone who believes in alchemy.

So why — why — are we trusting the future of scientific research to someone who doesn’t believe in scientific research about the future?

And I know these are criticisms that have been leveled against Cruz before; I’m not unique in my fulmination.  But I have to fulminate.  I have to, really, because 2014 was, unsurprisingly, the hottest year we’ve ever experienced — and that’s not a reference to any Kardashianic attempts to break the internet.  Just our species’ repeated attempts to break the planet.

Yet the people with guiding hands in our scientific policies choose to ignore that.  I’m not just talking about Cruz, though he makes an exceptional example.  His colleague Marco Rubio, who once said of climate change “I don’t think there’s the scientific evidence to justify it”, will be taking over leadership of the Senate Subcommittee on Oceans, Atmosphere, Fisheries, and the Coast Guard.





Rubio, who refuses to acknowledge that climate change, anthropogenic or not, could have catastrophic effects on the oceans and atmosphere (ironically threatening the Rubio’s hand-battered fish taco especial) is now presiding over the agencies responsible for the oceans and atmosphere.  How is this supposed to give me faith in the government’s ability to safeguard our country’s natural resources?  Our planet’s?

I can only point out the absurdity of the whole situation — no, I have to point out the absurdity of the whole situation.  I have to.  Really.  Because our country’s scientists deserve better than overseers who deny basic science.

The United States of America was arguably in the vanguard of every major technical innovation of the twentieth century.  We built, we flew, we coded.  We cracked the atom, conquered the moon, colonized the internet.  And we did these things with the help of our government, with the help of federal research money and the aid of the United States Congress.

What path do we have forward in the twenty-first century if scientific progress is held hostage by non-believers?


Disclaimer: I meant to post this two months ago, when it was actually timely, but my laptop’s graphics card all but went up in flames and I really didn’t want to type out the rest of the post of my phone.  Then I forgot about it, which is less of an excuse but probably easier to believe.  So apologies for my tardiness.

* * *

I’m not sure this blog is the place for celebrity tributes, but this is a big one.  For a couple of different reasons.

Robin Williams, to me, will always be two things simultaneously: he will be the Genie in Aladdin, a warm, congenial (eh? ehhh?) voice from my childhood, and he will be a large, hairy man, drenched in sweat and  screaming profanity on stage in an HBO special, ranting about golf and colostomy bags.  That one man could encompass both things in my mind — without even getting to Dead Poets Society or Good Will Hunting — speaks, I think, volumes about his versatility as a performer and entertainer.

The man’s a legend.  I’m going to reveal a couple of things I’m not particularly proud of about my childhood movie tastes here, but one of the first movies I remember laughing uproariously at was Flubber.  Eight-year-old Seth thought the “Make a Little Flub” dance was the most brilliant cinematic masterpiece since Ben Hur.  At the same time, I think the first time I actually realized, internalized, that I wasn’t going to live forever was watching Bicentennial Man at age eleven.

I’m not sure either film has well withstood the years since its release (I certainly haven’t rewatched either, and Rotten Tomatoes is… less than kind), but they still both were driven by one man.  One man, and such opposite emotions — emotions that, to this day, I can remember, even if I couldn’t tell you a single plot point of either movie.

The internet has already offered up all sorts of tributes and paeans to Williams, of course, and I’ve seen the following quote posted frequently.  It’s from the graphic novel Watchmen, set in a fairly dystopian alternate reality where Nixon has been president since the 70s, costumed superheroes are outlawed, and the world generally sits on the brink of nuclear disaster on a minute-by-minute basis.  Unlike your weekly Superman print, this is not an entirely odd place to find a rumination on the ironies of life, or a meditation on freedom and fatalism — albeit flavored heavily with giant naked blue dudes.  At some point amidst the novel’s stylized symbolism — some heavy-handed, but some deftly done — one of the main characters, Rorschach (who, like every other character, is a complete nutjob), tells the following story:

I heard joke once.  Man goes to doctor.  Says he’s depressed, life is harsh and cruel.  Says he feels all alone in threatening world.  Doctor says, “Treatment is simple.  The great clown Pagliacci is in town.  Go see him.  That should pick you up.”  Man bursts into tears.  “But doctor,” he says, “I am Pagliacci.”

It’s fitting for Williams, I’ll give it that.  His death certainly makes it seem that Robin Williams was a man like Pagliacci, who gave so much joy to so many others that he had none left for himself.

I can’t help but think back to what I felt when I was eleven years old and the credits rolled on Bicentennial Man.  It was an emptiness, a loneliness, that I had never felt before, like staring into a wall of black that never blinks and never ends.  I tried to squeeze my eyes shut and imagine what it would be like not to see, not to hear, not to smell, not to think.  I never got very far.  It was so overwhelming, this thought of doing — having — being — nothing that I was physically uncomfortable thinking about it.  That feeling hasn’t gone away.

I can’t, and won’t, argue that being afraid of my own mortality is anything similar to what Williams must have been going through.  It’s easy for me to sit here and type that, oh, I’m afraid of dying, he was afraid of living, both are challenges har har har — but that’d be pretty much as close to bullshit as I get on this blog.  I stared into the face of something I felt I couldn’t control and I balked, I ran away.  I’m still running away, but not every day.  Not every hour.  Being afraid of dying is a pretty human emotion, I’d like to think, and it’s not something I dwell on on a daily — or hell, monthly, even — basis.  Williams, on the other hand, stared into the face of something he felt he couldn’t control, for I don’t know how long, and it must have gnawed at him every second of every minute of every day until it ultimately devoured him.  I don’t know what that’s like, to be consumed by something like that.  I hope I’ll never know.

We are, each of us, Pagliacci in our own ways.  There’s a public Seth and a private Seth, a Seth that gives to others and a Seth that needs things for himself.  And over the last decade I’ve watched my friends, my loved ones, my tangential social acquaintances wrestle with their private selves, longer and harder battles then I’ve ever fought.

I want to close by saying if you need me, I’m hear to talk.  And if you don’t want to talk to me, you can pick up the phone and talk to someone else who cares: ‪1-800-273-8255‬.