Burning Polen

What if you were to somehow ignite the pollen that floats around in the air in spring? Other than being a really bad idea, what effect would it have?

Jessica Thornburg

The first thing we have to figure out is whether pollen is flammable. Some questions are best answered through academic research, but some questions can be answered much more quickly with a Youtube search. The answer is yes; pollen is extremely flammable.

(Note: Before we go any further, I want to point out that much of the US is under extreme drought, fire season is underway, and wildfires—90% of them caused by humans—kill firefighters every year. Please don't try to set pollen on fire.)

Now, back to the question.

What is fire, anyway?

Lots of materials oxidize when exposed to air. Bananas go bad, copper turns green, iron rusts. Fire is another kind of oxidation reaction. (In other words, our cars are always oxidizing; we just try to keep it from happening suddenly.)

Reactions like oxidation often go faster when the fuel has more surface area.[1] The more pieces you break something up into, the more surface area it has, which means that dust has a lot of surface area. Dusts can be very flammable; even normally non-flammable things like candy, milk, and iron[2]can—when converted to powder form—combust violently in a dust explosion. Pollen can explode, too; all those Youtube videos of burning pollen show miniature dust explosions.

When it burns, it releases energy, which brings us back to Jessica's question: What if all the pollen in the air suddenly (somehow) caught fire?

As anyone with seasonal allergies will tell you, pollen is everywhere. As anyone with seasonal allergies and giant stilts will tell you, high concentrations of pollen extend upward hundreds of meters above the ground.[3]

When pollen is burned, it releases energy. One gram of pollen releases 15 to 28 kilojoules of energy when burned, which means a handful of pollen contains roughly the same number of calories as a hamburger.

A grain of pollen weighs on the order of 10^-9 grams. In areas with a high pollen count, every cubic meter of air can hold thousands of grains of tree pollen. Fortunately for Jessica's scenario, this means that—when burned—the pollen floating in the air won't have much effect at all. It would raise the air temperature by a fraction of a degree—nothing more.[4]

The reason the pollen explosion is so mild is that the pollen is so finely spread out. What if we collected it together?

If you took all the pollen from the air across the United States, put it in a gigantic pile, and ignited it all at once, it would rapidly release on the order of 10¹³ joules of energy. That's about the yield of a very small nuclear weapon.

So look at it this way: Seasonal allergies may be bad, but they could be a lot worse.

$2 Undecillion Lawsuit

What if Au Bon Pain lost this lawsuit and had to pay the plaintiff $2 undecillion?

—Kevin Underhill

The bakery-cafe chain Au Bon Pain (with a few other organizations) is being sued. This is how much money the person suing them is demanding:

This is how much sellable stuff there is in the world:

This is the estimated economic value of all goods and services produced by humanity since we first evolved:

Even if Au Bon Pain conquers the planet and puts everyone to work for them from now until the stars die, they wouldn't make a dent in the bill.

Maybe people just aren't that valuable. The EPA currently values a human life at $8.7 million, although they go to great lengths to point out that technically this is not actually the value any specific person places on another person's individual life.[1] In any case, by their measure, the total value we place on all the world's humans is about $60 trillion—less than the total value we place on all the world's oil.[2]

But while people may be worthless,[3] we're hardly all there is on the planet. Out of all the Earth's atoms, only 1 out of every 10 trillion is part of a human.

The Earth's crust contains a bunch of atoms,^{[citation needed]} some of which are valuable. If you extracted all the elements, purified them,[4] and sold them, the market would crash.[5] But if you somehow sold them at their current market price, they would be worth ...

Oddly, most of this value comes from potassium and calcium, and most of the rest comes from sodium and iron. If you're going to sell the Earth's crust for scrap, those are probably the ones you should sift out.

Sadly, even selling the crust for scrap doesn't get us close to the numbers we need.

We could include the core,[6] which is iron and nickel with a dash of precious metals, but it turns out it wouldn't help. The amount demanded from Au Bon Pain is just too large. In fact, an Earth made of solid gold wouldn't be enough. The Sun's weight in platinum wouldn't be, either.

By weight, the single most valuable thing that's been bought and sold on an open market is probably the Treskilling Yellow postage stamp. There's only one known copy of it, and in 2010 it sold for $2,300,000. That works out to about $30 billion per kilogram of stamps. If the Earth's weight were entirely postage stamps, it would still not be enough to pay off Au Bon Pain's potential debt.[7]

If Au Bon Pain & co decided to be intentionally difficult, and pay their debt entirely in pennies, they would form a sphere that would squeeze inside the orbit of Mercury.[8] The bottom line is that paying this settlement would be, in almost any sense of the word, impossible.

Fortunately, Au Bon Pain has a better option.

Kevin, who asked this question, is a lawyer and author of the legal humor blog that reported on the Au Bon Pain case.[9] He told me that the world's most highly-paid lawyer—on an hourly basis—is probably former Solicitor General Ted Olson, who recently disclosed in bankruptcy filings that he charges $1,800 per hour.

Suppose there are 40 billion habitable planets in our galaxy, and every one of them hosts an Earth-sized population of 7 billion Ted Olsons.

If Au Bon Pain hired every Ted Olson in the galaxy to defend them in this case, and had them all work 80-hour weeks, 52 weeks a year, for athousand generations[10]...

... it would still cost them less than if they lost.

Pyramid Energy

What took more energy, the building of the Great Pyramid of Giza or the Apollo Mission? If we could convert the energy to build the Great Pyramid, would it be enough to send a rocket to the Moon and back?

Michael Marmol

No.

A Saturn V's fuel contains enough stored energy to lift up and stack about 20 pyramids worth of rock from the surface.

That's the simple physicist-style answer, based on calculating the energy required to lift idealized blocks of stone against the Earth's gravity.[1] In practice, pyramid construction wasn't so simple. Thanks to friction, the Egyptians probably expended more energy dragging the stones across the ground than lifting them upward—and the "lifting upward" involved a lot of friction, too.

Most of the energy they expended was lost to the heat of friction, but about 10¹² joules of it remains in the Great Pyramid, stored as gravitational potential energy. If all this energy were liberated and—somehow—used to accelerate an Apollo spacecraft ...

... it wouldn't be enough to launch it to the Moon.

On the other hand, the reverse probably wouldn't work, either.

But maybe we're making the wrong kind of comparison. Why did Michael—like many others—compare the pyramids to the Apollo program in the first place? Perhaps it's simply that they both look like they took a huge amount of work—and maybe that's the best way to compare them.

The Great Pyramid, according to one analysis, took an average of 13,200 people 10 years to construct. The Apollo project took an average of about 200,000 people, working over a similar period of time, to launch six Moon landings and another 6-10 missions using the same equipment before and after—which, if you divided it up equally,[2] is about 15,000 hours each. In other words, each Apollo mission took about the same amount of work as each pyramid.[3]

There are all kinds of ways we could measure the energy that went into various megaprojects, but we end up making a lot of subjective judgment calls about what counts as part of the project. Instead, let's go back to the simple idea of gravitational potential energy, and see how the Great Pyramid compares to other structures by that measure.

The gravitational energy locked up in the Great Pyramid—on the order of 10¹² joules—is more than in even the biggest modern skyscrapers. The Burj Khalifa may be huge, but it's mostly empty space. Egyptian pyramids, on the other hand, are solid rock nearly all the way through.

However, the Great Pyramid isn't the human structure with the highest "gravitational potential energy" score. The Three Gorges Dam, built across the Yangtze River in China, is both taller and heavier than the Great Pyramid. It contains an order of magnitude more potential energy than the pyramid in its concrete and steel alone—without even considering the far larger potential energy of the water behind it.

The Great Pyramid has a few other big competitors. The former Fresh Kills Landfill probably had more gravitational potential energy, as do various other giant dams. The Great Pyramid of Cholula in Mexico has a larger volume than the pyramid at Giza, though probably weighs slightly less and has less potential energy.

But these are all dwarfed by our biggest rock-and-dirt-lifting projects: mines. Mining involves lifting even more matter against gravity than building concrete dams, pyramids, or landfills. Humans have put a huge amount of industrial power into digging mines, so it's no surprise that the biggest mines involve 10¹⁴ to 10¹⁵ joules of gravitational energy—orders of magnitude more than the biggest aboveground structures. After all, open-pit mines are basically reverse pyramids:

These projects are pretty big. However, the Dutch have envisioned something bigger.

In 2011, a Dutch writer launched Die berg komt er, a semi-serious plan to build an artificial mountain in the Netherlands. Some versions of the plan would involve moving far more material than in even the largest mines, and the immense weight would probably cause the Dutch countryside to sink—which isn't really something they need more of.[4]

This plan is obviously impractical. Fortunately, someone else has come up with a better one.

A group of Germans, led by architect Jakob Tigges, have decided that Berlin already has an artificial mountain. Built on the site of the former Tempelhof Airport, "The Berg" towers 1,071 meters above the surrounding landscape, edging out the Burj Khalifa as the tallest manmade structure on Earth. It has a website, a Facebook group, photos, testimonials, and tourism information.

Now, nobody can see this mountain. But supporters insist that it's there.

If only the Egyptians had thought of that one.