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## Niagara Falls is over two miles high!

Let’s watch a clip from the movie Superman II, which I saw in the theater in 1980:

Great acting, right?

From the time (Δt) that the kid is in the air, we can determine how high Niagara Falls (ostensibly) is.  I get Δt = 27 s, so the height of Niagara Falls is given by

H = ½ a Δt2 = ½ (9.8) 272 = 3572 m.

Wow!  That’s big…more than 3.5 km.  That’s over two miles high!

(It’s actually higher than this, if we notice that Superman didn’t even catch the kid at the very bottom.)

In point of fact Niagara Falls is 51 m high.  Only half a football field.  In the real world, it would take the kid (neglecting air resistance) all of 3.2 seconds to hit the rocks below.  Superman has no time to change his costume; Lois has no time to scream for help.  3.2 seconds, then splat.

Let’s ponder the magnitude of the error the filmmakers made here.

MOVIE: 3572 m

REALITY: 51 m

This is a 7000% error.  That has to be some sort of record.

To put it into perspective, it would be like listing Shaquille O’Neal’s height as 165 yards, instead of 7’1″.  This is fun!  In the world of Superman II, Oslo has a population of 43 million, Gone With the Wind has a running time of almost 12 days, the moon is almost as massive as the Earth, and the average cat weighs 630 lbs.

The movie supposedly grossed \$190,000,000.  We now know, however, that (given the 7000% inflation trend in Superman II) the move only grossed \$2,700,000.

This makes Superman II the greatest flop of all time.  For some reason, though, when I saw it around my 12th birthday, I liked it.  Maybe that’s because it was really my 840th birthday?

## All the ways—

What scares you more: that I will talk of death, and injustice, and spiritual annihilation?  Or that I will explain how the equation

Pfi  = ∑ Γ(S)

Admit it.  You want death.  You want injustice.

You want spiritual annihilation.

I get it, I get it.  Math is an annoyance; math is anathema.  As it did for the learn’d astronomer, math makes you unaccountable tired and sick.

Maybe math scares you.  Or worse—maybe math bores you.  Fear you can take, and anxiety in equal measure; but boredom, never.  It wasn’t time but boredom that sunk Ozymandias into the lone and level sands.  Because—

Because (you say) math is about numbers.  That’s it.  It’s just numbers.  By enumerating, you take away a spark.  That which can be counted, can be dismissed.  A mathematician is a bean counter with a pocket protector, somewhere on the spectrum, digitizing nature, walling off the soul with a wall of 1’s and 0’s.

But it isn’t true.

I could plead that mathematicians don’t usually think of numbers.  They think about patterns, symmetries, interconnectedness.  They see math in the petals of a daisy, and in the predator/prey cycle of lynx and snowshoe hares.  Math is in the strength of nanowires, and the delicacy of hoar frost, and the oomph of an engine, and the whorls of a Spirograph.

I could plead that math is about connections, structures.  Math is the study of logical systems.  Numbers are beside the point.

Beside the point.

I’m looking right now at the white-board in my office.  Ignore the calendar with a picture of Crater Lake, and ignore the poster of Han in Carbonite, and ignore the Albert Einstein action figure, and the pamphlet which says “Welcome Aboard Marine One.”  Focus on the white-board itself: it’s covered with equations, in red and green and blue, with doodles, starts and stops, arrows and spirals, letters both Roman and Greek.  There are graphs of velocity vs. time.  There’s a derivative, and an integral.  There’s Newton’s 2nd Law, half-erased.

There are no numbers on the board.

I could plead still, but here is what I know: that math is beauty, and that the whole world is math.  Here in my ivory tower, I adhere to the Mathematical Universe Hypothesis, which posits that the multiverse is itself is “just” a mathematical structure.  It’s not infinite turtles, but math, all the way down.

Jump if you like: you’ll never hit the bottom.

And what of the equation I gave?  What does it say?  To whom does it speak?

It comes from a paper I wrote, across a gulf of years and disciplines.  It says, in English, that the probability of going from quantum state A to quantum state B is the sum of all the products of closed-loop amplitudes that include A and B.

I am A.

You are B.

To get from me to you, we have to count all the ways we can interact, including ways that go backwards from you to me.

We add up all the ways.

And in the end you don’t have a number, but possibilities.