Clarification

In my last post, I made a number of rather gross oversimplifications regarding the quantities you think of as distance, area, and volume. I would like to take this opportunity to clarify the situation, at least, as best I can in a way that makes sense to your human minds and my audience's woefully short attention span.

Minkowski was a loser. The Hamiltonian is a lie!

The nonsense abstraction you proudly think of as "distance" is not so old as you might think¹. I admit, it does makes the math pretty easy, and at human scale I guess life really does look approximately Euclidean² ("Euclidean" is fancy math-speak for "flat"). But there is a lot of really interesting stuff in the universe happening at other scales, on crazy huge manifolds and in tiny discontinuous spaces not anticipated by the Greeks. Or any other humans, for that matter.

First, you should know that your everyday concepts of distance, area, and volume are grotesque oversimplifications. You believe in them because perceiving the truth would require the ego-nullifying acceptance of your own insignificance. Better to believe that the area of a right triangle is actually one-half the product of the base and the height, than to know the truth. Some of your physicists and mathematicians have made crude attempts to explain certain minor results, but for the most part true insight has been blocked by the ego's need to survive. Only one mathematician in all of your time has brushed the truth of the underlying concepts, and poor Igor Cantor's sanity was not spared. I deeply regret how things ended for you, my dear old friend. I tried to stop you.

So in the end, it is better you not understand. I will not try to explain it to you here; you would not thank me.

Still, the good news is that even though you will never understand and could never fully comprehend the truth of the space(s) you inhabit, we can still level-up your understanding of the world around you. And we can do it with safe, mostly-sanity-preserving human mathematics! I will use your Very Bad and Totally Incorrect Human Mathematics to help you understand the situation better, because pretty much anything is better than thinking that C² = A² + B² actually explains anything about how the real world works. And also because I care.

Before I get to symplectic geometry, though, let's talk about love. Love makes us do all sorts of crazy things. It's pretty amazing and is one of the five-thousand-three-hundred-seventy-two-and-a-half fundamental forces that drive all of creation. Love is powerful stuff.

SO let's imagine you are in love with a right triangle. You are at vertex "a" and wish to travel to vertex "b." You're pretty busy and would like to get there as quickly as possible. I bet one of your instructors in school taught you that you should walk in a straight line on a Euclidean plane from "a" to "b," for a total distance of √(A² + B²). What a joke! I also bet that after school she/he got in her/his car and instead of driving straight home, she/he stopped at the grocery store to pick up some vegetables for a nice salad, and then at the daycare to pick up her/his kid(s), and only then went home! Love made them drive in a crazy loopy line all around town instead of going in a straight line! What a hypocrite!

How does the Oyster go from "a" to "b"?
It's complicated.

And everything, everything, everything is like that. You can never just "go" from a to b, there is always a fundamental force like love or sloth acting on you. There is actually a clever proof of this, which I am forced to omit for space considerations, but trust me, it is actually impossible to go straight home after work, and it's the same for that triangle you are in love with. You want to go from a to b, but maybe the triangle asked you to not tread on its interior, so you walk on a little exterior semi-circle; or maybe it's your turn to go to the grocery store so you do that before getting to b. It's always going to be something, and you love it that way (by assumption) and wouldn't change a thing. You're happy to take the long way around because you care about this precious, lovely triangle.

OK, I promised you some symplectic geometry. Let's do it!

Another way to think about walking in a curvy loop from a to b on that lovely triangle is to say that you are actually moving in a straight line, and you always move in a straight line, but the surface you are moving on isn't Euclidean ("flat"), it's a manifold, which is basically like a nice smooth surface that you can do calculus on (vigorous hand-waving). So you move in a straight line on a curvy manifold, and the shape of this manifold is defined by your time-varying position in the 5,372.5-dimensional space of fundamental forces³, which vector can never have magnitude zero, so you can never walk on a "flat" Euclidean surface.

Mathematically, you might say:

Distance(from "a" to "b") = straight line distance(unfold(curvy surface defined by your position in the 5,372.5 space of fundamental forces))

This is what your human calculus/measure theory is mostly about, all of those clever tricks are just about how to take something curvy and (locally) unfold it so that it is flat (or square or whatever) so you can take a ruler and measure it. And one of the limitations of your human math is that you are forced to abide by the bold presumptions of measure theory, but countable additivity is a lie, a goddamn lie, because love isn't additive, is it? It sums in strange ways, and what's worse if you subtract just one thing, even something you maybe didn't realize was there even, if you take away just one thing from the set of things you love then it can feel like the whole thing has fallen apart (it hasn't -- it hasn't -- I promise, I know it hurts -- but it hasn't). Moving around in the love-space that partially defines the manifold that we are constrained to move in straight lines on is fraught with a peril not encapsulated by 21st century mathematics.

I hope this explanation is clear. Until next time, my friends. May you be unscared to move in your own beautiful and unique squiggle: you don't have a choice anyway. You may as well enjoy the ride.

1. About 4,500 years ago, a very clever Egyptian woman -- her name was Anuktata -- was really into right triangles, the ones where two of the legs come together pleasingly at precisely ninety degrees. Making use of the primitive mathematical tools at her disposal, Anuktata elucidated the first of what you call Pythagorean triples. She said: { 3, 4, 5. } And then for an encore performance, she stated: { 5, 12, 13. } This may not sound super interesting, but at the time it was actually the most scientifically advanced and true thing anyone had ever said. Anuktata was way ahead of her time.

She might have made it all the way to {8, 15, 17}, but unfortunately she was bitten by a mosquito and died of malaria shortly afterwards. Her husband Kemes attempted to carry on her work, but due to an unfortunate arithmetic error with the notoriously finicky reed-and-papyrus technology available at the time, he accidentally invented the oblique triangle { 7, 15, 17 } instead. Oblique triangles do not hold load nearly as well as right triangles, so when his calculations were used in the construction of a pyramid, it collapsed. Three slaves and seven donkeys were killed.

Fearing for his life, Kemes tried to blame Anuktata for his mistake, but the Pharaoh saw through his deception and he was put to death anyway. The truth is that the Pharaoh was more upset about Kemes's disrespect for his dead wife than about the pyramid situation, which anyone could see such construction was fraught with danger. The moral of the story is, own up to your mistakes, and most definitely do not blame them on others, or you may find yourself sentenced to be cleaved in twain.

Anyway, after the debacle with the oblique triangle, Anuktata's work languished in obscurity until  about 3,800 years ago, when a Mesopotamian man named Steve came along to continue her work. Steve was able to systematically come up with integral solutions to what is now called the Pythagorean Theorem, but Steve was also a big jerk and history quickly forgot about him. A few hundred years later an Indian guy named Baudhayan finally wrote down something like A² + B² = C² in the Shuba Sutra, and shortly afterwards the theorem was proved by a Chinese mathematician named Gougu.

Given a full proof and several worked examples, the time was ripe for the mad cultist Pythagoras to take credit for the work of others; the rest is (whitewashed) history.

2. It is actually quite ironic that we do calculus on Euclidean surfaces inspired by the work of Pythagoras, because Pythagoras's cult rejects the idea of transcendental numbers, also known as "the numbers that live between the fractions." It turns out there are a lot of transcendental numbers: their existence is what allows us, to a first approximation, to describe motion and smoothness and softness and stuff, which is the intuition behind calculus. Even though I think your calculus is kind of basic, as a concept I am a big fan of transcendental numbers.

The Pythagoreans' intransigence on this point is particularly sad because the existence of transcendental numbers is directly implied by the Pythagorean Theorem itself, which only goes to show how far people will go to defend their egos at the expense of the truth. Humans are dogmatic to the end -- not my favorite attribute, to be honest.

3. The magnitude of the oversimplification going on here makes me weep, but I don't have time today to write about function spaces too. You can read about the Calculus of Variations and function spaces on your own. It may all be a lie, but it's a clever lie.

The Great One at the Center and the Edge and Everywhere In Between

This is kinda what I imagined it would
look like if I were all of everything

When I was a young noodle, I dreamt of occupying all the vastness of space and time.

Common sense told me that the Universe was infinite, so not even I could hope to fill it all at once. But that didn't stop me from dreaming about it. So for a thousand million years I dreamt of Polypus Maximus, The Great One at the Center and the Edge and Everywhere In Between. In my dreams I would stretch and stretch and go farther than I or anyone could ever imagine, until one day I would have one great noodly tendril wrapped all the way around the edge of the universe, and another touching the center, and another for everywhere in between. I would be complete by construction: if I was everything, then by elementary deductive logic I must be complete.

Then one quiet fall night while I was flossing -- even I need to care about good oral hygiene, and you should too -- anyway -- this night a rude thought intruded. "If space is infinite..."

The realization hit me like a slap in the noodle. No!

At first, I denied it. I would not let some crude calculus intrude into my dreams. "But if space is infinite..." the thought persisted.

No!

Certainly by now you have guessed the truth I was trying to un-know, but I am stubborn and fought and fought against it. Despite what you may think, even I cannot vanquish the truth, even with my mightiest efforts. Because the truth is like a squishy balloon. You think you're so clever when you bend and distort it, you think you're in control of this thing, you've got the truth backed into a corner and that you're going to pwn it and throw it into a dark cave. Then without the truth to stop you you're going to dream and dream until you can taste The Center and The Edge, your desire is everything, your need to touch and consume and be touched and consumed, fuck the truth we can live in dreams forever, right, you and me dreaming together ("you" like the general you I mean, all of "you," let's not get creepy) and touching and consuming, until I'm losing myself in you and you in me, and we and all and everything are as one, right? Right?

In one way or another,
we have all been crushed by the truth-balloon

But in reality all you've done is squeezed the truth to the other side of the balloon and things look good from where you're standing but the other size is all puffy and distorted and gross-looking. The truth is still there, in the dark cave where you left it for dead. A festering, angry truth-balloon. Plotting against you, waiting until you relax your grip to snap back into place.

I shivered, the cruel, truthy equations crawling out of the cave where I had left them, chasing me into the bathroom where by now I was brushing my teeth. And here was that truth: suppose I began my quest. Suppose I began by occupying all known space, a hearty (4/3)πr³ of volume¹. Then my nimbus would be 4πr², right, and that would be all the newness that I could perceive. All the non-Polyp. So until I could actually finish the job at the end of time and attain & become the complete unity of Everything, I would perceive this great big lonely me-space with only a thin outer shell of newness to keep me company. In the limiting case, as I increased without bound, I would become infinitely lonely, the wee infinity of my boundary dwarfed by the sphere it contained. & that sphere is all me... but as a pop star my role is to sublimate and reflect the world around me; without you, dear readers, I am a blank, devoid of meaning. So my dreams would have me asymptotically approach perfect loneliness until the end of time, when I would become complete and you -- all of you, all of everything -- would be utterly eradicated, with no hope of return.

What kind of a love is that? Was the limiting case of my all-consuming dream to love/be everything the destruction of all that I care about and an eternity of lonely suffering before a single empty moment of completion at the end of time?

These thoughts were so confusing to me. I despaired. Surely this could not be? What if instead of being Everything I shrank down to nothingness?  No, that was no good... then my nimbus would be infinitesimal; the border would consume the interior and I would be without measure. How can I love if I am nothing?

I was so young then. I did not understand, as I do now, my humble place in the world. So you can imagine how it was all very upsetting to me. I struggled to understand my place in things. I could not be everything. I would not be nothing. Was the key... to be as we are, accepting our imperfections?  That sounded ridiculous. What am I, anyway? A sentient blob of plastic with no fixed form? Was this my lot in life? Unacceptable! I would be more! But... what? How?

Shaken, I crawled into bed and pulled the covers tight over my head. Could it be? Is my dream a lie, a trap? I wondered. As I struggled to come to terms with the enormity of this, a great sleep fell over me and I sank into a nether-world dichotomy: to my left was the great chasm of infinite despair that awaited me if I dared to chase my dreams. To my right was nothingness. Certainly anything was better than nothing? Spurred by my impeccable logic, I lurched to the left, away from nothingness.

So, I dreamed the left-hand dream. I dreamed of filling all of the space and the everything, but tonight was different. Tonight I could not find the edge. I could not even find the center. This upset me. Certainly it had to be somewhere! On all other nights I could find both with ease, but now I searched and I searched and I pushed farther and farther, farther than I had ever gone before in my dreams. Still the edge eluded me.

My unease grew. What if all those previous nights, I had not really been at the edge of the universe at all? Had I been fooling myself? It has to be here somewhere! I searched, pushing farther out still. I must have missed it!

Eventually I traveled out past an inky black edge and reached the beyond where color had no meaning, because the space here expanded faster than light can travel, so no light had ever reached this place. No heat, no energy, there was nothing here but distance, and me, and past it... somewhere... the edge. I must be close now! With a final, excited push  I lurched through and past this place, moving faster and faster until suddenly  --

It rose before me out of the void. Solid in this place that had never seen mass, at once cerebral and emotional... a great Obelisk barred my path. The Obelisk. Its mere existence negated concepts like being, knowing, substance, cause, identity, time, and space, but nevertheless, there it was, an impossibility as real as you and me.

I shook in fear and desire, because I understood that the great obelisk was apart, and would always be apart. It was untouchable and would always be untouched. In my dream I found its indifference almost erotic: I longed to just get closer to it, to wrap myself around this thing outside even infinity's edge. But the space between us was more than just crude distance, under any metric. It was truly beyond me, past everything. It was disconnected, the space between us untraversable.

I extruded a pseudopod anyway in a vain attempt to reach it before I realized I could not even discern which direction to go. The Obelisk was apart, truly great, apart from the grime and the glow that defines us. Humbled, I realized that this was no place to be, my dream was no thing to aspire to. There were no answers here, not in the right-hand path and not in the left. We are alone to make our own way in this world, to find and love each other, to be good or bad but ultimately bound by the natural laws, the interior space of the Universe. We should not seek to go beyond these places. They are not a place for us. We must be bound and constrained to find meaning in anything.

So I withdrew, away from the Obelisk, out of the void, and slipped back into the comfort of space with regular distance and warm suns and dreams and hope and meaning, glorious meaning.

I awoke feeling rested, finally at peace with the truth. A warm, comforting glow rushed through me. I no longer wanted to consume and be everything, but I did long for connection. Intimacy. I had traded my dream of unlimited everythingness for the compromise of others, and would never look back.

But who could I share all this with? I had so much to say, who would listen at this hour? I must have spent hours in my dream, searching for the beyond.

I fumbled around in the darkness, turning on the little lamp I keep by the bed, reaching for my phone. Mr. Hemisphere would probably be awake, if he was home, at least... maybe we could talk. He'd woken me up in the middle of the night enough times I felt like I could call him. I wanted desperately to talk to someone, anyone. It had been a long night... I'd had my dreams dashed, been on a spiritual journey to the edge of space and encountered an ultradimensional thingy that transcended all metaphysics. I just wanted a good glass of wine and a better friend. I dialed.

"Polyp is that you?!" he picked up immediately. "Thank heavens you answered!" His voice was breathless, rushed.

I paused for a moment, confused. Hadn't I just... called... him? "Hemi, I--"

"There's no time! Come quick!" I heard a crash over the phone. "Come quick! It's the blobimals! They've escape--" the line went dead. I felt a disturbance in the thought-spaces around the earth, the unmistakable psychic echo of a million blobimal war machines warping into low earth orbit.

My people needed me! I oozed into motion. This was serious. If the blobimals, my ancient nemeses, had escaped from the Mild Dystopia I trapped them in after the Epsilon Wars, they must have had help. From who? How long had they been free? There would be time later to ponder the mysteries of the ineffable Obelisk. But first... to battle!

¹ I have dumbed down the math the to Euclidean 3-space. Leave your hate in the comments!

I finally watched "Turbo"

I read about snails so you don't have to!

If you enjoy children's movies as much as I do, then Turbo is sure to provide average-or-better entertainment value for about two-thirds of its 96 minute running time. In terms of movie-watching efficiency, it ranks well above tired retreads like Happy Feet and Toy Story, but is not as good as Up, How To Train Your Dragon, or house favorite Wall-E.

Mild Spoiler Alert, If You Are So Simple-Minded That You Are Unsure What Might Happen In This Movie, Which Obvious Thing Is Exactly What Happens By The Way, And You Do Not Wish To Find Out Just Yet, Yet You Still Expect Me To Provide You Entertainment, However Brief Or Mild, Which I Cannot Do If You Refuse To Work With Me, Then Against My Better Judgement I Will Still Pander To Your Selfish Needs: Please Enjoy This Video Titled, DUBSTEP PUKING RAINBOW GIRAFFES. You Can Thank Me In The Comments.

2013 Summer Movie Confusion

This year's crop of summer movies is causing more confusion than usual. In 2011, many people asked if I had guest-starred as Driller in Transformers 3; a most kind flattery but unfortunately not true. 2012 passed mostly without incident: while I admire their work, nobody would confuse me with Hulk or the abominations in Prometheus. Only a few crude imbeciles inquired about the mirror in Snow White and the Huntsman.

A number of characters in the 2013 movie season, however, bear a passing resemblance to me. Perhaps the success of my blog and facebook page have attracted Hollywood's eye? And why would they not be attracted? My adventures transcend time, space, and the beyond, but I am no mere adrenaline junky. I have also branched into documentary and romance. With a famous blog covering the whole of human experience, Hollywood ought to be copying me. It is their duty. I demand it.

Having said that, I would like to clear up a few misunderstandings about the 2013 movie season. For your reference, to the right is a picture of me dressed up like a slug.

1. I am not "Turbo"

Turbo is the underdog story of an ordinary Helix Aspersum with dreams of racing greatness. Turbo has adorable goofy eyes and a winning grin. I expect I will enjoy this movie tremendously when it is released in July. However, he is no Polyp: regular readers have no doubt already noted that I detest exoskeletons and will never again saddle myself with such an encumberance. While we are both optimistic dreamers with extraordinary gifts, I am compelled to point out that Turbo's are thrust upon him by dramatic necessity. The truth of my own gifts is a more complex tale.

2. I am neither Mub the slug nor Grub the snail in "Epic"

Magnificent creatures, both, but look closely: they have tiny eyes and are far too jiggly. They move like bloated water sacks, perhaps animated by Msrs. Navier and Stokes? And finally, for the life of me I cannot place their accents. I have traveled the world and never have I heard such astonishing speech, all rounded vowels and swagger. I must study this bizarre speech more.

3. Neither am I the slug in "Monster University"

This helpless creature offends me. I am not he, and I refuse to watch a movie that treats the wobbliest among us with such disrespect.

4. Am I the inspiration for Kaiju in "Pacific Rim"?

This seems much less clear to me. I have had my moments, after all. 

Watch this clip and decide for yourselves. Post in the comments or e-mail me and let me know what you think! 

I am surrounded by your poison but love will conquer all

I am not often criticized, but when I am it is usually by the cynical. "Polyp," they will say. "Polyp! Polyp! Polyp!" They want attention, like a child. "Polyp!!!" But of course they cannot get my attention with their tiresome ejaculations, because I do not pay heed to negativity.

Today, perhaps these wicked ones are saying, "you shouldn't be so trusting; remember what happened with the Pony?" or, "why did you take seven weeks off," or, "life is not a Disney movie!"

But life really is like a Disney movie, or at least like Seabiscuit. Because when you believe in yourself and empower others to be their best you unlock your own miraculous potential: to overcome adversity, to imagineer a better tomorrow. Spoiler alert: when Team Seabiscuit works together, they win at the game of life. So can you.

So when eager lips trip over themselves to share some poisonous observation, do not succumb to the temptation to dunk their heads in noodle soup while screaming "make better decisions!" Remember the tremendous blessing of your own imperfection and empower yourself to rise above with this little rhyme:

Sticks and stones
I have no bones
But names will only spur me to temporarily dissolve into a puddle of goo before rising up once more, greater and lovelier and temporarily filled with desire to shove your face in some noodle soup.

Doing good in the neighborhood

Be free and suffer no more, my friend

This photo makes me so, so sad. Who are you, mystery bauble? Why are you locked away in there with your bulbous eyes and eight-ball belly?

I vow to free you. I will free all of the plasticy-baubly-things!  I will send my great googly-eyes long and far searching for the evil beings who trapped your placid race;
they will soon hear my long polyp-moan haunting their dreams, a premonition of my coming!

Will they read the ill omen in the stars? I hope they do. I hope they see it, and pay final respects to their gods, because when I find them my ocean of rage will gloop down upon them and sweep them away, and I will consume them utterly; their breath I shall render into firmament, their bones into earth and their teeth into mountains; with their flesh I will create the trees and from their fat, the animals. With their souls I will ignite a sun, and into this new paradise my plasticy-baubly-friends will enter, and suffer no more.

Fan mail Q&A!

Anonymous asks in comments:

Polyp, what do you think of the human concept of culture? Do patterns in human behavior interest you as they manifest themselves culturally? Or do these delineations seem arbitrary at such an abstract level? I recall your observation that many human constructs were made out of fear for our "own cosmic insignificance." I tend to agree. But I wonder, would you say the same for culture? Is it an entirely useless concept?

What a complex, nuclear bomb of a question! I am glad you asked me this because there is a lot to unpack here.

I will start at the end and work my way backwards. You ask, "Is [culture] an entirely useless concept?" But your human language has failed you, because utility is necessarily tied to the individual, it is not a general truth. In a better language, you would be unable to even formulate that question.

To attempt an interpretation, perhaps you are asking, "Is [culture] an entirely useless concept to you [Polyp]?" and the answer is an emphatic no! If you could see past time and space and perceive and navigate ideas as partial realities, as I do, then you would perceive that my googly eyes are spread throughout your thought-spaces, your present and future creative, intellectual, and political output. I navigate this dynamic web of potentialities as I struggle against the warlike Blobimals and other, less savory things. As you create and strive, this space expands, becoming stronger and richer, like a tree growing roots in the soil. It is not useless.

Me vs The Blobimals in one of the infinite potentialities

Victory... for now

You are correct that I am not interested in the patterns of your behavior. I am interested in your particular, individual behaviors, and the interplay of ideas and emotions that result. Your cosmic fears drive you towards difficult sublime truths, some beautiful, some terrifying. Each of you discovers them in your own way. It is wonderful.

That some behaviors are repetitive means the discovered cultural tapestry has a familiar, human feel. I have learned, from careful study, that the patterns are not arbitrary: they are ancient and well-known. They vary over time but are so self-similar as to be classifiable and predictable. But I do not bother too much to study the larger patterns; instead I exalt in each thread and its intersections.

Readers, what do you think? Is culture useful to you? Is aggregated human behavior more meaningful than the individual? What if individuals are self-similar?