Archive for February, 2014

WARNING: Spoilers abound!

Do not read further if you haven’t seen the wonderful, awesome The Lego Movie!

There are two kinds of good movies.  The first kind is a movie you enjoy while watching; you appreciate the acting, the writing, the set design.  You come out of the theater thinking, that was good.  I’d recommend that.  In the past six months, I’ve seen many of these so-called Good Movies of the 1st Kind.  Examples include The Dallas Buyer’s Club, Rush, Captain Phillips, the second Hobbit movie, and the second Hunger Games movie.  I liked them all.


A metaphor for the everyman

But then there is a Good Movie of the 2nd Kind—a movie which leaves you jacked up on adrenaline, with a big goofy smile on your face, and ideas buzzing around the inside of your head.  A movie where you come out of the theater thinking, when am I going to go see that again?  I need to see that again.  What just happened?

Don’t get me wrong; a GM2ndK is not necessarily a happy, fun movie.  Saving Private Ryan was for me a GM2ndK; for weeks I could not get the first half hour (Omaha Beach) out of my head.  Schindler’s List was also a GM2ndK.  So was A Clockwork Orange, and Magnolia, and Paths of Glory.

So, too, The Lego Movie.

Unless you’ve seen the movie, you won’t believe it.  You won’t have the context, the conceptual framework, the raw materials from which to grasp the idea: that The Lego Movie is as profound and philosophical as any movie you’ve (probably) ever seen.

Oh sure, the movie is beautiful to look at.  The animation is unique and charmingly quantized and pixilated.  The pace is frenetic, action packed.  The worlds depicted are stunning, goofy and marvelous.  The jokes are non-stop: I laughed out loud two or three times a minute for 100 straight minutes.

So, I liked the movie.  But this post wasn’t meant to be a movie review.

My broader point is that the movie resonated with me, personally, philosophically, because it so closely matches my own world view.


The message of the movie is that there are two (seemingly) diametrically opposed ways of playing with Legos.  In the first camp are the conformists, who follow instructions to the letter, never have an original thought, and prefer a world of rigidity and order.  The head conformist is Lord Business, who wants to spray Krazy Glue on every Lego in the universe so that nothing ever changes.

To me, Lord Business represents the Abrahamic God, the God of the Old Testament.  The God of one single, rigid construction, exactly the way He designed it.  Don’t go against God’s plan (or the plan of Lord Business).  There is only one way the world (or worlds) can be, and if you oppose that plan—if you don’t follow the instructions—then you have committed heresy.  You will be melted.  There’s no place for you in such a conformist world.


The God of Abraham

The other way of playing with Legos is the way children play with them: with unbridled imagination.  Sure, you can buy a Millennium Falcon Lego set and construct it as the instructions describe.  But you can ignore the instructions, too, and your play is just as valid.  Want to put Batman on the Millennium Falcon?  Sure; go for it.  Want to have Superman and Gandalf team up to battle a robot pirate?  Why not?  If you can imagine it, then you can do it, just as long as some adult doesn’t come down and spray the pieces with glue.

That’s what organized religion does: it sprays us with glue.

To me the world of organized religion is limiting, stifling.  The idea that there’s an omnipotent being that controls every aspect of everything is not comforting to me; it is horrifying.  Theologians mumble about free will and wave their hands reassuringly, but what good is free will if you’re still constricted by God’s plan?  If God has everything worked out, then you’re stuck to the world with Krazy Glue; your life is supposed to be lived in a single way and you’ll never be able to ignore the instructions.  You’ll never get to ride Unikitty into Middle Zealand and have tea with the Green Lantern.  Sorry, but you’re an average, run-of-the-mill Lego piece and that’s all you’ll ever be.

But imagine: suppose that there are an infinite number of universes, each with its own parameters, its own structure.  In such a multiverse, anything you can imagine is true.  There are still rules (each universe obeys its own laws of physics, just as Legos cannot escape their own block-like, quantized nature) but beyond those rules, anything goes.  And imagine there is no Lord Business that commands you to think in a certain way.  Imagine if you had the freedom to do as you will.

Here’s a table, to make the metaphor(s) more explicit:

In the movie… …is a metaphor for
A Lego person a human
The Lego world you’re in the universe you’re in
All of the possible Lego Worlds the multiverse
Quantized nature of Lego blocks the laws of physics
Krazy Glue God’s plan
Lord Builder (the Father) a rigid conformist deity
The Child the deity that any of us could be, using imagination
Instructions Rigid moral codes
“Everything is awesome” “Everything is awesome”

We are indeed trapped in the universe that we find ourselves in (we can’t get away from our quantized nature, alas) but we can at least imagine the other worlds, and dream, and find inspiration from them.  We can live our lives the way we like.  This isn’t anarchy; it’s freedom.  This world view doesn’t preclude morality; we shouldn’t put our hands into other people’s Lego Worlds, and mess the pieces up, and break their Lego constructions.  But we should be able to look at other people’s constructions, and value them, even love them.  If you want to have Batman marry Han Solo, and have them ride off into the Old West sunset (riding on Unikitty, no doubt) then I shouldn’t judge.  There is no Lord Business.  There is only what you can build, and what I can build, and what you can imagine, and what I can imagine.  We should not judge each other but embrace each other’s constructions.  Everyone’s trapped by the laws of physics, but no one’s trapped in their own minds; there are no laws that can ever force our imaginations to conform.

If God exists, then he’s a child, and wants us to play in all the worlds, and be free.  He wouldn’t even own a tube of Krazy Glue.

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I was watching Dr. Who the other day and came across a physics mistake so common I thought I’d address it here.  The mistake is this:

Black holes suck you in like a vacuum cleaner!

The setup: in Dr. Who [2.8] “The Impossible Planet”, the good Doctor and Rose meet the crew of a ship who are on “an expedition [to] the mysterious planet Krop Tor, impossibly in orbit around a black hole.” [Wikipedia]  That phrase “impossibly in orbit” made me almost spit out my drink while watching the show.

Black holes have event horizons.  I get it.  Even light cannot escape.  I get that, too.  But why does that mean I cannot orbit a black hole?

OK, time for a little general relativity.  Einstein figured out, between 1905 and 1915, that gravity is “just” a warping of space-time.  Matter causes the space-time around it to curve; the curvature of space-time determines how matter moves (insofar as objects in the absence of gravitational forces follow geodesics).  The formulas that link the distribution of matter to the curvature of space are Einstein’s equations:


This expression is compact and might seem relatively simple, but it’s not.  Gαβ and Tαβ are components of tensors, which are like vectors, but worse; they’re really 4×4 matrices.  So this equation is not one equation, but 16 different equations, since α and β can take on any of four values each.

What do all those letters stand for?  Gαβ is a component of the Einstein tensor, which tells you about how space-time is curved; the indices α and β can be any of four values in a 4D space-time.  (If you’re mathematically inclined, the Einstein tensor can be related to the Ricci scalar, the Ricci tensor, and the Riemann tensor.)  Tαβ is a component of the stress-energy tensor, which basically describes how matter/momentum/energy/stress/strain is distributed in a region of space-time.  So here’s another way to visualize Einstein’s equations:


The cause (mass) is on the right; the effect (the curvature of space-time) is on the left.

So what does this have to do with black holes?

One of the first solutions discovered to the Einstein equations is called the Schwarzschild solution, which applies to a spherically symmetric gravitational source.  The solution gives you a “metric” (essentially, a geometry) that is almost the same as “flat” space-time, except for a pesky (1–2GM/c2r) term.  But that pesky term has a strange implication: when that term equals zero, the solution “blows up” (i.e. becomes infinite).  Space becomes so curved that you essentially have a hole in the fabric of space-time itself.

When does this happen?  It happens when R = 2GM/c2, as one line of algebra will show.  This is called the Schwarzschild radius.  The Einstein equations predict that something weird and horrifying happens when a mass is squeezed down to the size of its Schwarzschild radius.  Current understanding is that the mass would then keep going, and squeeze itself into a point of zero radius.  Literally, zero.  (I did say it was weird and horrifying).

Incidentally, the Schwarzschild radius is exactly the radius you’d get if you set the escape speed for an object equal to the speed of light.  So this means that not even light can escape this super-squeezed object.

And here’s where various misconceptions start to creep in.

Another name for the Schwarzschild radius is the event horizon.  It’s a boundary of no return:  if you cross it, you can never go back.  But that’s all it is: a boundary.  There is not necessarily anything physical at the event horizon.  You might never know that you had crossed it.  Remember, all the mass is at the center.

Here’s how I “picture” a black hole:

black hole

Now, if I am outside the event horizon, what would I see?  Well, nothing from inside the event horizon could reach me (hence the term “black”) but I might see Hawking radiation.  I would certainly see gravitational lensing: the bending of distant light around a black hole.  Here’s a cool picture of gravitational lensing in action (artists conception only!) from Wikipedia:


Let’s say the Sun were a black hole.  Its event horizon would be around 3 km.  As long as we never got closer than 3km, we could do what we like.  We could fly in, fly out, orbit the black hole as we please.

Would the black hole “suck us in”?  Sure, in the same way that the Sun sucks us in already.  There is a strong pull of the Sun on the Earth.  And there would be a strong pull on our hypothetical spaceship.  But change the Sun to a black hole, and the pull would not get any stronger.  That is the key point that most people miss: black hole gravity is not somehow “stronger” than ordinary gravity.  There is just gravity; that’s it.  Change the Sun to a black hole, and the Earth would continue in its orbit, and nothing would be any different.  Except for, maybe, the lack of light.

Why was the planet Krop Tor’s orbit impossible?  Astronomical black holes (created by stellar collapse) have a lot of mass; when there’s a lot of mass hanging around, things tend to orbit them.  That’s what you’d expect.  It would only be impossible if somehow the orbit crossed the event horizon multiple times during its trajectory.  But of course, the show didn’t mention this.

I want to end my rant on GR with a suggestion: that there are two kinds of sci-fi: science fiction, and “sciency” fiction.  The first kind tries to get the science right, and makes an effort to be possible (if not plausible).  The second kind throws sciency words around in an effort to appeal to a certain demographic.  Basically, “sciency” fiction is fantasy, set in outer space.  When seen in this light, Dr. Who has more in common with Lord of the Rings than it does with 2001.

Don’t get me wrong: I love Lord of the Rings, and I love Dr. Who.  Just don’t call it science fiction.

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