How far would a tungsten countertop descend if I dropped it into the Sun?

Michael Leuchtenberg

Not very far.

With its high melting point, tungsten is a good[1]Except that the word "good" implies that you have some kind of goal you're working toward, which—given how strange the thing you're doing is—I'm not sure about. choice for a sundiving countertop.

The first problem would be sunlight. As the countertop approached the Sun, it would heat up. Tungsten has the highest melting point of any element, but the Sun is one of the meltiest things in the Solar System. When the countertop got within a couple of solar radii, it would liquify.

If you protected it with a heat shield of some kind, or dropped it from a sundiving spaceship, it could enter the Sun's atmosphere relatively intact. In this case, some interesting physical effects would destroy it.[2]"Some interesting physical effects would destroy it" summarizes the answers to a large percentage of the questions submitted to this blog.

Because the Sun is so heavy, anything that falls to its surface will be accelerated to a tremendous speed by its gravity. A falling countertop would reach speeds of over 600 km/s—0.2% of the speed of light. (Our rockets can only accelerate spacecraft to 10-20 km/s.)

From the countertop's point of view, particles from the Sun's atmosphere would be slamming into it at 600 km/s. These particles would pack quite a punch.[3]From a particle physics point of view, the individual protons would have energy of about 2 keV. When the countertop got within about a few thousand kilometers[4]I don't want another unit-related word to mentally keep track of, but it's always seemed a little weird that we don't call thousands of kilometers "megameters". of the Sun's surface, these collisions would start delivering more energy to the countertop than the sunlight.

The collisions would fling individual tungsten atoms away from the surface—a process called sputtering. Between the sputtering and ordinary heating from the impacts, the countertop would start to absorb a lot of energy very quickly.

If the countertop were larger, it could penetrate into the Sun's photosphere—the first layer beneath the "surface"—and potentially trigger a solar flare.[5]For a scientific discussion of this, see the article Impacts of comets onto the Sun and coronal mass ejections. For a science fiction discussion of this, see Stephen Baxter and Arthur C. Clarke's 2005 novel Sunstorm. But as it is, it wouldn't even make it through the Sun's atmosphere—it would be vaporized somewhere in the Sun's chromosphere.

This brings us around to a key question:

Who the hell has tungsten countertops?

Sure, it has good heat tolerance. But I'd be nervous about using tungsten as a food-preparation surface.

In September of 1994, a French soldier drank wine from a rifle barrel. Fifteen minutes later, he started having seizures. He was rushed to the hospital and treated for "acute tungsten intoxication"—the first known case in medical history. He reportedly made a full recovery, although concentrations of tungsten were present in all his body tissues for weeks.

The lesson here is to use normal materials. Michael, just make your countertops out of granite and don't drop them in the Sun.

And if you're a French soldier, please just drink wine like a normal person.

If all the seas were one sea,
What a great sea that would be!
If all the trees were one tree,
What a great tree that would be!
If all the men were one man,
What a great man that would be!
If all the axes were one axe,
What a great axe that would be!
And if the great man took the great axe,
And cut down the great tree,
And let if fall into the great sea,
What a great splish-splash that would be!

... How great would all of these things be?

—John Eifert (quoting a Mother Goose rhyme)

If all the seas were combined into one sea, it would look pretty much like the Pacific Ocean, only a little bigger.

The poem's tree, axe, and human are more interesting.

The tree

Real trees can't grow taller than around 130 meters, thanks to physical limits on their ability to transport water. If they found a way around those limits, they'd face issues of fundamental physical strength; a kilometers-tall tree would crush itself.

Let's set aside these limits, and imagine that we built a single standard tree out of all the material in all the world's trees.

For our "standard tree," we'll use the oak tree from the Sylva Foundation's OneOak project. The project extensively documents every detail of a single oak tree. As part of the project, the tree was cut down in 2010. Frankly, I'm not sure what to make of the whole thing, but it's as good a candidate as any for our model "standard tree".

The OneOak tree was 23.9 meters tall and weighed 14.385 tons.[1]Slightly more of the mass was in the branches than the trunk. By comparison, one paper estimates that the world's forests have an aboveground plant mass of about 470 billion tons.

If—ignoring the physical constraints—we combined this mass into a single tree, modeled on the OneOak, the trunk would be two kilometers in diameter. The upper branches would stretch about 75 kilometers above the surface—most of the way to space.

The human

If we used the same approach to combine every living human into a single body—again, ignoring the obvious physical constraints—that person would be close to 3 kilometers tall.

Proportionally, the person would have grown slightly less than the tree.

The axe

How many axes are there in the world?

Thanks to multiple meanings of the word "axes", this is a hard problem to Google.[2]That, and the fact that it's a weird statistic that no one has any real reason to try to gather data on even if they could find a way to do so. Instead, let's try to get a reasonable guess through Fermi estimation.

Since there's no central clearinghouse of axe-related information, I thought I'd try asking friends how many axes they had.

But this might miss a lot of axes; for example, some axes—like fire axes—are owned by organizations. To get a slightly fairer sample, I asked a bunch of friends around the country to estimate the number of axes and number of humans in their general vicinity.

Some people were in houses with sheds, and had a 2:1 human-to-axe ratio. Other people were in large offices with hundreds of people and at best one or two fire axes. The average seemed to be around 50:1—much lower than I expected.[3]I grew up in a house with a wood shop, and we always had a roughly 1:1 axe-to-human ratio.

Of course, surveying random Internet-connected people who I know is hardly representative; rural people probably have more axes, while the very poor might not have any. But it also wouldn't make sense for there to be substantially more axes than people, if for no other reason than that humans can only really use one axe at a time.

But absent any other data, I'm guessing the ratio of humans to axes is probably somewhere between 50:1 and 5:1.

This means that our combined axe would be a little small for our combined person. It would be only a little over half a kilometer long—barely more than a flimsy hatchet.

If an experienced axe user can chop down an eight-inch tree in 15 minutes, then chopping down our giant tree—if the rate is proportional to the axe size and square of the tree's diameter—would most likely take a few weeks of chopping.

The fall

The tree would weigh between 1% and 10% as much as the Chicxulub asteroid that killed the dinosaurs.

It would strike the ocean with much less speed than the Chicxulub asteroid, and the energy release would be much less substantial. However, it would still be moving at kilometers per second, and would be able to displace a gigantic amount of water.

The Chicxulub impact created a giant tsunami; the buried layer of jumbled sand mixed with a fossilized forest it left along the coast of the Gulf of Mexico was a crucial clue in discovering the location of the crater.[4]For more on this discovery, I can't recommend the book T. Rex and the Crater of Doom highly enough. It's written by Walter Alvarez—one of the researchers who found the first evidence for the impact—and is one of the best pieces of popular science writing I've ever read.

There have been some beautiful simulations of the Chicxulub tsunami. The exact details of the tsunami depend on a lot of factors, but it seems safe to say that waves at least tens or hundreds of meters high would inundate every coastline and destroy virtually every coastal city and many farther inland.

In other words, the Mother Goose poem in John's question probably wouldn't wipe out the human race, but it would probably be the deadliest single disaster in our species's history. Even by the ghastly standards of old childrens' fairy tales, that's pretty bad.

Axe law

In closing, I offer my favorite piece of axe-related legal trivia:[5]That's not a long list, but the things on it are all pretty memorable.

Lawyer Kevin Underhill, of the legal blog Lowering the Bar, hilighted the wonderful 1998 case People v. Foranyic. In this case, he writes, appeals court ruled "that there was probable cause for police to detain someone they see riding a bike at 3 a.m., carrying an axe."

So if you're two miles tall and heading toward the coast to cut down the world's only tree ...

... watch out for cops.

I just moved into a new apartment. It includes hot water but I have to pay the electric bill. So being a person on a budget ... what's the best way to use my free faucet to generate electricity?

David Axel Kurtz

You could build a tiny hydroelectric dam in your tub.

It would generate power, though not very much of it. The formula for power is pressure times flow rate.[1]Or, alternately, flow rate times density times height. Since bathtubs are pretty shallow, the pressure at the bottom isn't very high, so this works out to around two watts of power, or about 25 cents per month.

You can get more power if you increase the pressure of the water passing through the generator. To do this, you could increase the depth of the water. If you have two floors in your apartment, you could have the water column stretch from the second to the first floor, generating at least ten times the pressure and ten times the power.[2]This is similar to the rainwater scheme discussed in article 23. In effect, the local authorities would be paying to pump the water up to your apartment, and you're getting some of that energy back when you let it flow back down.

Could you use the faucet to pump the water up arbitrarily high, and get more and more power out of it as it falls back down?

No. First, you couldn't pump the water arbitrarily high. Household faucets have a pressure of around 4 atmospheres.[3]60 PSI. That's about 4000 millibars, if you measure your plumbing with an old barometer. You can lift water about 10 meters per atmosphere of pressure, which means that a household faucet can only pump water up by about 40 meters.

Second, as you can probably guess by looking at the above picture, pumping the water up 40 meters with water pressure and then back down doesn't accomplish anything—you can just hook the faucet up to your device, and let the water pressure drive the generator directly. In either case, for a bathtub faucet, this works out to almost 200 watts, or $25 per month.

You'd have to make sure your plumbing could handle the water. If your pipes get plugged up and stop draining, the faucet could fill your house in a matter of days. And either way, eventually someone from the city would probably show up to ask why you're using 40 tons of water every day.

And really, with California suffering through its worst drought in history, this system might earn you some dirty looks. Sure, if you live far away from California, it's not like your water would have gone to ease their drought, but wasting a gigantic amount of water (and investing a bunch of money) to save a few dollars on your electricity bill might come across as a little rude.

A bathtub's flow rate is five or six orders of magnitude less than that of a river, but it's still a lot of water. Could we put it to a less selfish use?

There's a common piece of advice that says you should drink 8 glasses of water a day. No one really knows where this advice came from; people claim you should drink anywhere from 2 to 12 glasses of water daily,[4]For some reason, the saying only ever uses even numbers; a web search turns up lots of tips about six or eight glasses per day, but few advising you to drink seven. and none of them have any real evidence behind them. The only real solid advice I've heard is that if you're thirsty, you should drink some water.

If we stick to the "8 glasses of water" standard, then a bathtub faucet provides enough drinking water to sustain about 10,000 people indefinitely. In other words, the city of Manhattan could survive on the water from just 150 bathtubs.

But if your goal is to save money on your electric bill, there's a much more lucrative option.

Single servings of bottled water sells for a dollar or two per half-liter. A lot of bottled water comes from municipal sources—that is, it's tap water. Bottled water isn't necessarily about the water; often, people are paying for convenience or because there's an issue with their water supply. Whatever the reason, however, there's no reason to let Coca Cola keep all the profits.

If you bottled the water from your bathtub faucet and managed to sell each bottle for \$1.50, you'd make \$72 per minute—\$38 million every year.

Then you won't have to worry about your power bill.

What would happen if the Earth's rotation were sped up until a day only lasted one second?

—Dylan

If this is going to happen, I hope it doesn't happen late in the afternoon next Friday.

The Earth rotates,^{[citation needed]} which means its midsection is being flung outward by centrifugal force.[1]Which is still a real thing. This centrifugal force isn't strong enough to overcome gravity and tear the Earth apart, but it's enough to flatten the Earth slightly and make it so you weigh almost a pound less at the Equator than you do at the poles.[2]This is due to several effects, including centrifugal force, the flattened shape of the Earth, and the fact that if you go far enough toward the pole in North America people start offering you poutine.

If the Earth (and everything on it) were suddenly sped up so that a day only lasted one second, the Earth wouldn't even last a single day.[3]Either kind. The Equator would be moving at over 10% of the speed of light. Centrifugal force would become much stronger than gravity, and the material that makes up the Earth would be flung outward.

You wouldn't die instantly—you might survive for a few milliseconds or even seconds. That might not seem like much, but compared to the speed at which you'd die in other What If articles involving relativistic speeds, it's pretty long.

The Earth's crust and mantle would break apart into building-sized chunks. By the time a second[4]I mean, a day. had passed, the atmosphere would have spread out too thin to breathe—although even at the relatively stationary poles, you probably wouldn't survive long enough to asphyxiate.

In the first few seconds, the expansion would shatter the crust into spinning fragments and kill just about everyone on the planet, but that's relatively peaceful compared to what would happen next.

Everything would be moving at relativistic speeds, but each piece of the crust would be moving at close to the same speed at its neighbors. This means things would be relatively calm ... until the disk hit something.

The first obstacle would be the belt of satellites around the Earth. After 40 milliseconds, the ISS would be struck by the edge of the expanding atmosphere and would be vaporized instantly. More satellites would follow. After a second and a half, the disc would reach the belt of geostationary satellites orbiting above the Equator. Each one would release a violent burst of gamma rays as the Earth consumed it.

The debris from the Earth would slice outward like an expanding buzzsaw. The disk would take about ten seconds to pass the Moon, another hour to spread past the Sun, and would span the Solar System within a day or two. Each time the disc engulfed an asteroid, it would spray a flood of energy in all directions, eventually sterilizing every surface in the Solar System.

Since the Earth is tilted, the Sun and the planets aren't usually lined up with the plane of the Earth's equator. They'd have a good chance of avoiding the buzzsaw[5]I keep reading this as "Buzzfeed". directly.

However, Next Friday, April 25th, the Moon will cross the plane of the Earth's equator (as it does every two weeks). If Dylan sped up the Earth at this moment, the Moon would be right in the path of the resulting planetary buzzsaw.

The impact would turn the moon into a comet, sending it rocketing from the Solar System in a spray of debris. The flash of light and heat would be so bright that if you were standing at the surface of the Sun, it would be brighter above you than below. Every surface in the Solar System—Europa's ice, Saturn's rings, and Mercury's rocky crust—would be scoured clean ...

... by moonlight.

At what speed would you have to drive for rain to shatter your windshield?

Daniel Butler

Fast.

Raindrops are tiny. Even in the heaviest rainstorms, the water in the air weighs less than the air itself (which is one of several reasons you can't swim upward in a rainstorm). Even at very high speeds, they can't break a windshield via their momentum alone.

Under ordinary circumstances, raindrops don't damage car windshields at all. However, they can destroy the windows of supersonic aircraft.

Here's what happens when a raindrop hits a glass surface at high speed:

When the droplet makes contact with the surface, a shockwave travels back up through the droplet.

Normally, this shockwave would move at the speed of sound within the liquid—about 1300 m/s, four times faster than in air. However, at high impact speeds, this shockwave actually moves substantially faster than the speed of sound in water.

The water is squeezed between the incoming drop and the glass surface, which makes it squirt sideways in all directions. These jets of water can move even faster than the original (already supersonic) droplet, and even faster than the shockwaves we mentioned.

One paper ran a simulation of water droplets hitting a surface at 500 m/s (about Mach 1.5), and found that the water sprayed out from the point of contact at over 6000 m/s—Mach 18.[1]That's a pretty simple way to expel material at 6 km/s. I wonder if anyone's ever tried to come up with a spacecraft propulsion system using it ...

The sharp pulse from the shockwave can crack glass. The highest pressures are found in the ring around the edge of the droplet, and only exist for a tiny fraction of the impact.

In addition to the direct downward pressure, the water jetting sideways can cause damage, too. If the material has any microscopic holes, cracks, or bumps, those jets can strike them and create new cracks or widen existing ones.

Even at high speeds, a raindrop won't create a bullet hole on its own—but a long series of supersonic droplets would start to eat away at the glass, cracking and pitting it like sand.[2]This type of "erosion" can also cause damage to steam turbine blades. Eventually, the windshield could fail catastrophically.

Luckily, cars can't drive at Mach 1 without lifting off, so your windshield is safe from ordinary rain. On the other hand, if you're driving under a thunderstorm with strong updrafts ...

... the precipitation can smash your windshield at any speed.

My daughter—age 4.5—maintains she wants a billion-story building. It turns out not only is that hard to help her appreciate this size, I am not at all able to explain all of the other difficulties you'd have to overcome.

Keira, via Steve Brodovicz, Media, PA

Keira,

If you make a building too big, the top part is heavy and it squishes the bottom part.

Have you ever tried to make a tower of peanut butter? It's easy to make a little tiny one, like a blobby castle on a cracker. It will be strong enough to stay standing. But if you try to build a really big castle, the whole thing smushes flat like a pancake.

The same thing happens with buildings. The buildings we make are strong, but we couldn't make one that went all the way up to space, or the top part would squish the bottom part.

We can make buildings pretty tall. The tallest buildings are almost 1 kilometer tall, and we could probably make buildings 2 or even 3 kilometers tall if we wanted, and they would still be able to stand up under their own weight. Higher than that might be tricky.

But there would be other problems with a tall building besides weight.

One issue would be wind. The wind up high is very strong, and buildings have to be very strong to stand up against the wind.

Another big problem would be, surprisingly, elevators. Tall buildings need elevators, since no one wants to climb hundreds of flights of stairs. If your building has lots of floors, you need lots of different elevators, since there would be so many people trying to come and go the same time. If you make a building too tall, the whole thing gets taken up by elevators and there's no space for regular rooms.

Maybe you can think of a way to get people to their floors without having too many elevators. Maybe you could make a giant elevator that takes up 10 floors. Or you could make fast elevators that work like roller coasters. Or you could fly people up to their rooms with hot air balloons. Or you could launch them with catapults.

Elevators and wind are big problems, but the biggest problem would be money.

To make a building really tall, someone has to spend a lot of money, and no one wants a really tall building enough to pay for it. A building many miles tall would cost billions of dollars. A billion dollars is a lot of money! If you had a billion dollars, you could rent a giant spaceship, save all the world's endangered lemurs, give a dollar to everyone in the US, and still have some left over. Most people don't think giant towers a few miles tall are important enough to spend a lot of money on.

If you got really rich, so you could pay for a tower to space yourself, and solved all those engineering problems, you'd still have problems making a tower a billion stories tall. A billion stories is just too many.

A big skyscraper might have about 100 floors, which means it's as tall as 100 little houses.

If you stacked 100 skyscrapers on each other to make a mega-skyscraper, it would reach halfway to space:

This skyscraper would still only have 10,000 floors, which is way less than your billion floors! Each of those 100 skyscrapers would have 100 floors, so the whole mega-skyscraper would have 100 times 100 is 10,000 floors.

But you said you wanted a skyscraper with 1,000,000,000 floors. Let's stack 100 mega-skyscrapers to make a mega-mega-skyscraper:

The mega-mega-skyscraper would stick out so far from the Earth that spaceships would crash into it. If the space station were heading toward the tower, they could use its rockets to steer away from it.[1]They'd probably get pretty grumpy after having to dodge your tower repeatedly, so you might want to launch fuel and snacks out the window with a rail gun as they go by. The bad news is that space is full of broken spaceships and satellites and pieces of junk, all flying around at random. If you build a mega-mega-skyscraper, spaceship parts will eventually smash into it.

Anyway, a mega-mega-skyscraper is only 100 times 10,000 = 1,000,000 floors. That's still a lot smaller than the 1,000,000,000 that you want!

Let's make a new skyscraper by stacking up 100 mega-mega-skyscrapers, to make a mega-mega-MEGA-skyscraper:

The mega-mega-MEGA-skyscraper would be so tall that the top would just barely brush against the Moon.

But it would only be 100,000,000 floors! To get to 1,000,000,000 floors, we have to stack 10 mega-mega-MEGA-skyscrapers on top of each other, to make one Keira-skyscraper:

The Keira-skyscraper would be pretty close to impossible to build. You would have to keep it from crashing into the Moon, being pulled apart by the Earth's gravity, or falling over and smashing into the planet like the giant meteor that killed the dinosaurs.

But some engineers have an idea sort of like your tower—it's called a space elevator. It's not quite as tall as yours (the space elevator would only reach partway to the Moon), but it's close!

Some people think we can build a space elevator, but other people think it's a crazy idea. We can't build one yet because there are some problems we don't know how to solve, like how to make the tower strong enough and how to send power up it to run the elevators. If you really want to build a gigantic tower, you can find out more about some of the problems they're working on, and eventually become one of the people coming up with ideas to solve them. Maybe, someday, you could build a giant tower to space.

I'm pretty sure it won't be made of peanut butter, though.

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]Assume a spherical pyramid in a vacuum ... 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]Which is a bit of a stretch, since launching a second Apollo mission probably lets you reuse a lot more of your work on the first one than building a second pyramid. is about 15,000 hours each. In other words, each Apollo mission took about the same amount of work as each pyramid.[3]The Apollo program was unpopular at the time; people thought it was a waste of money. While it's easy to remember only the excited children gathered around TVs to watch the first Moon landing, the truth is, spending public money on space exploration has never been all that popular with the general public. For all we know, the pyramids were just as unpopular with the Egyptian public in their time. They probably weren't built by slaves, but that doesn't mean everyone was happy about them.

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]For this reason, most serious proposals involve a hollow mountain. I mean, serious compared to the other ones.

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.

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]Note that they don't say whether they assume that amount would be higher or lower. 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]Come to think of it, that explains a lot.

But while people may be worthless,[3]I'm rounding down. 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]This is just one of many reasons that this idea wouldn't make sense in practice. The reason many elements (like U-235) are valuable is that it's hard to manufacture or purify them, not just because they're rare. and sold them, the market would crash.[5]Both in the sense that the supply would cause a drop in prices, and the sense that the market is like 20 miles above the mantle and you just removed the crust supporting it. 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]It's down there. 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]Also, the stamps would probably be less valuable now that there is literally an entire planet of them, but that's the least of Au Bon Pain's problems.

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 fate of this sphere of pennies is left as an exercise for the reader. The fate of Mercury is that it would fall into the pennies and disintegrate. 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]And which we encountered in Question #90. 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 a thousand generations[10]This scenario assumes that the former Solicitor General reproduces asexually....

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

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]This is part of what's behind the Diet Coke and Mentos effect, although the actual details are a bit more boring complicated. 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]Candy, Milk, and Iron was my unsuccessful self-published follow-up to Jared Diamond's Guns, Germs, and Steel. 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]This Spanish study found pollen concentrations increased with altitude up to 600 meters. This follow-up, by a group of high school rocket enthusiasts in Madison, found that pollen increased for the the first few hundred meters, then dropped off dramatically at even higher altitudes. (Also, their rocket sampled pollen by deploying two pollen collectors dubbed—adorably—"bees".)

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]Although it would definitely come as a nasty surprise to any bees carrying it.

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.

Could you get drunk from drinking a drunk person's blood?

Fiona Byrne

You would have to drink a lot of blood.

A person contains about 5 liters of blood, or 14 glasses.

If your blood is more than about half a percent alcohol, you stand a pretty good chance of dying. There have been a handful of cases of people surviving with a blood alcohol level of above 1%, but the LD₅₀—the level at which 50% of people will die—is 0.40 (0.4%).

If someone had a BAC of 0.40, and you drank all 14 glasses of their blood in a short amount of time,[1]Hey, there's a 50% chance they were going to die anyway. you would throw up:

You wouldn't throw up because because of the alcohol; you'd just throw up because you're drinking blood. If you somehow avoided vomiting, you would have ingested a total of 20[2]Thank you to Conor Braman, among others, for correcting a missing zero in the original version of this calculation. grams of ethanol, which is the amount you'd get from a pint of beer.

Depending on your weight, drinking that much blood could raise your own blood alcohol level to about 0.05. This is low enough that you could legally drive in many jurisdictions, but high enough to double your risk of an accident if you did.

If your BAC is 0.05, it means only 1/8th of the alcohol from the other person's blood made it into yours. Supposing that after you drank all this blood, someone killed you and drank your blood,[3]It's only fair. they would then have a BAC of 0.006. If this process were repeated about 25 times, there would be fewer than 8 molecules of ethanol left in the last person's blood. After a few more cycles, there would likely be none;[4]By homeopathic standards, this is still quite concentrated. they'd just be drinking regular blood.[5]Like a loser.

Whether there's any alcohol in it or not, drinking 14 glasses of blood wouldn't be fun. There's not a huge amount of medical literature on the subject, but anecdotal evidence from online forum posts suggests that any normal person who tries to drink more than about a pint of blood will vomit:

If you drink blood regularly, over a long period of time the buildup of iron in your system can cause iron overload. This syndrome, which sometimes affects people who have repeated blood transfusions, is one of the few conditions for which the correct treatment is bloodletting.[6]Others include PCV and PCT.

Drinking one person's blood probably wouldn't cause iron overload. What it could give you is a blood-borne disease. Most such diseases are caused by viruses that can't survive in the stomach, but they could easily get into your blood through scratches in your mouth or throat as you drank.

Diseases you could get from drinking an infected person's blood include hepatitis B and C, HIV, Hantaviruses, and Ebola. I'm not a doctor, and I try not to give medical advice in these articles. However, I will confidently say that you shouldn't drink the blood of someone with Ebola.

That said, drinking or eating blood is not unheard of. It's a taboo in many cultures, but the British eat "black pudding", which is largely blood, and there are similar dishes all around the world. Maasai pastoralists in east Africa once lived mainly on milk, but also sometimes drank blood, drawing it from their cattle and mixing it with the milk to form a sort of extreme protein shake.

So the bottom line is that drinking enough of someone's blood to get drunk would be very difficult, probably quite unpleasant, and might give you some serious diseases.

In the end, the blood itself would do awful things to your body long before the booze ever could.

I was watching this video and was wondering: How many birds there would need to be for gravity to take over and force them into a gargantuan ball of birds?

—Justin Basinger

The video shows starlings, birds which ...

• • gather in giant flocks of sometimes more than a million animals
• • can talk
• • sound like R2-D2, though not as much as bobolinks do

The gravitational force between adjacent starlings is small. If two birds were flying half a meter apart and tried to go perfectly straight, they would fly for over a thousand kilometers before the gravitational force between them finally steered them into colliding.

Side note: The following is the first sentence from a journal article on starling metabolism:

We trained two starlings (Sturnus vulgaris) to fly in a wind tunnel whilst wearing respirometry masks.

I really think the paper should have stopped there; no matter what their results were, they can't possibly improve on the achievement they opened with.

Anyway, back to gravity.

To calculate the gravitational force from a whole flock of starlings, we need to know the flock's density.

Conveniently, a 2008 paper in Animal Behavior gathered some detailed statistics on starling flocks. The highest density they saw was about half a starling per cubic meter.[1]0.54 (•)>m^-3 If the birds weigh about 85 grams each, that means the air in a starling flock weighs 25 times more than the starlings themselves.[2]This makes a certain intuitive sense. If they were that much heavier than the air between them, it's hard to imagine how they'd be able to stay airborne by pushing off of it with their wings.

This means that the air's gravity is 25 times stronger than the starling cloud's gravity, and it's the air's gravity that will dominate the collapse.

The collapse of giant clouds of gas or birds is governed by the equation for the Jeans instability. It suggests that in order to undergo collapse, a cloud of uniform room-temperature air full of starlings would have to be much larger than the Earth to collapse.

The gas cloud's gravity would be very weak, so the starlings would probably have a hard time flying until they got used to it. (Birds can fly in zero g—or, at least, they flap around in confusion. But, to be fair, that's how I'd react if I were abruptly and without warning yanked from my bed and tossed into the air in a zero g airplane cabin.)

Such a cloud wouldn't form in the first place without some extra compression. To collapse naturally under its own gravity, the starling cloud would need to be so large that it would engulf the Solar System. When it did collapse, it would heat up, and the starlings ...

... would become a star.

Did WWII last longer than the total length of movies about WWII? For that matter, which war has the highest movie time:war time ratio?

—Becky

World War II was longer than the movies about it.

To tally up World War II movies, you could start with Wikipedia. The site lists about 400 unique titles across their various lists of World War II films.

Wikipedia is often the best place to find obsessive list-makers and categorizers. However, in the area of movie categorization, they have nothing on the people who tag plots on IMDb.

Before we finish answering Becky's question, let's take a brief side trip into the strange IMDb tagging world.

IMDb categorizes films with plot keywords. These words (or phrases) can be extremely specific, and cover a bizarre range of topics. For example, say you want to find all movies whose plot contains the following elements: "Nun", "laser", "binoculars", "electric shock", and "shot in the chest".

IMDb will tell you that there is one movie whose plot contains all those elements: The 2009 Steve Martin film The Pink Panther 2. To find other strange combinations, try clicking on a tag, then scrolling down to the "Refine by Keyword" section at the column on the right. Have fun.

Often, the people tagging articles aren't exactly, um, disinterested scholars. Skimming the other keywords for any innocuous search makes it pretty clear that many people are using the database to catalog every movie containing a scene that satisfies their particular prurient fascination.[1]There's nothing new about this, although the internet makes it easier; quicksand enthusiasts, for example, have been cataloging movies containing quicksand scenes since the VHS days.

But IMDb is more than just a fetish database.^{[citation needed]} Other obsessed people—like history buffs—have contributed their own sets of IMDb tags. The end result is a staggeringly comprehensive database of plot elements—which brings us back to Becky's question.

IMDb lists 4,893 films tagged with "world-war-two". The list contains full-length movies, TV episodes, short films, and the occasional miniseries. I downloaded a random sample of these entries and found that the average run time was 95 minutes, which means the entire collection probably has a combined length of a little over 300 days. World War II lasted six years, for a war:film ratio of about 7:1.

This ratio is hard to beat; no other multi-year war has been the subject of nearly as many films. This is understandable; we're talking about bloodiest conflict in human history right in the middle of the golden age of Hollywood.

However, some very short wars come close to beating it. The Six Day War—fought in 1967 between Israel and a coalition comprising Egypt, Syria, Jordan—is a good candidate. IMDb lists 13 films tagged with "six day war", and the Israeli film database EDB lists an additional four. However, the Six Day War movies are heavy on short TV episodes, so their war:film ratio doesn't quite edge out World War II based on these lists.

It's probably impossible to prove conclusively which war has the higher ratio. There no doubt exist other films about the Six Day War in various regional collections which I couldn't find—and the same is certainly true of World War II.

There are other wars which might score even higher on Becky's scale. The Indo-Pakistani War in 1971 is a good candidate; it was a short war (13 days) in the middle of a conflict heavily covered by India's film industry. IMDb lists five films about the related 1971 Bangladesh war, and it's likely that many of the Bollywood films about the broader India-Pakistan conflict touch on it. My guess is that the 1971 war probably has a higher film:war ratio than World War II, but I wasn't able to find specific data to support this.

Maybe the most interesting potential answer to Becky's question is the Anglo-Zanzibar War. This one-sided colonial war, fought between the British Empire and the Sultinate of Zanzibar, lasted only 38 minutes.[2]The short version is that Zanzibar's sultan died and his nephew, Khalid bin Bargash, moved into the palace. The British, who had a more pro-British candidate in mind for the position, sent warships and demanded Khalid step down. He refused, so the British warships bombarded the island, killed hundreds of Zanzibaris, and set the palace on fire. Khalid fled and the British installed a puppet government. Only 38 minutes passed between the start of the shooting and the British capture of the palace. Given how short it was, it would only take a single film about it to make it the undisputed champion.

However, I couldn't find any films about this war. I'm sure one exists somewhere; if you can find it, feel free to tag it on IMDb. There's nothing there at the time of this writing, but maybe there will be soon.

Alternately, if Becky can find a historic site with some link to Zanzibar, has a cell phone camera which can record for more than 10 minutes, and feels like making an independent film ...

... she can answer her own question once and for all.

As plastic is made from oil and oil is made from dead dinosaurs, how much actual real dinosaur is there in a plastic dinosaur?

Steve Lydford

I don't know.

Coal and oil are called "fossil fuels" because they formed over millions of years from the remains of dead organisms buried underground. The standard answer to "what kind of dead stuff does the oil in the ground come from?" is "marine plankton and algae." In other words, there are no dinosaur fossils in those fossil fuels.

Except that's not quite right.

Most of us only see oil in its refined forms—kerosene, plastics, and the stuff that comes out of gas pumps—so it's easy to imagine the source as some uniform black bubbly material.

But fossil fuels bear fingerprints of their creation. The various characteristics of these fuels—coal, oil, and natural gas—depend on the organisms that went into it and what happened to them. It depends on where they lived, how they died, where their bodies ended up, and what kinds of temperature and pressure they experienced.

The dead matter carries its story—altered and jumbled in various ways—for millions of years. After we dig it up, we spend a lot of effort stripping the evidence of this story away, refining the complex hydrocarbons into uniform fuels. When we burn the fuels, their story is finally erased, and the Jurassic sunlight that was bound up in them is released to power our cars.[1]Through photosynthesis, organisms used sunlight to bind carbon dioxide and water into complex molecules. When we burn their oil, we finally return that CO₂ and water to the atmosphere—liberating millions of years worth of stored carbon dioxide all at once. This has some consequences.

The story carried by rocks is a complicated one. Sometimes pieces are missing, discarded, or transformed in a way that misleads us. Geologists—both in academia and the oil industry—work patiently to reconstruct different aspects of these stories and understand what the evidence is telling us.[2]My favorite book about Earth science, Walter Alvarez's T. rex and the Crater of Doom, is a firsthand account of the research that determined what killed the dinosaurs. The story is told not as a contest between rival academic theories, but as the unraveling of a mystery through detective work.

Most oil comes from ocean life buried on the seabed. But the poetic idea that our fuels contain dinosaur ghosts is in some ways true as well. There are a few things required for oil to form, including quick burial of large amounts of hydrogen-rich organic matter in a low-oxygen environment.[3]Because, in a sense, oxygen will cause the fuel to burn.

These conditions are most often met in shallow seas near continental shelves, where periodic nutrient-rich upwellings from the deep sea cause blooms of plankton and algae. These temporary blooms soon burn themselves out, dying and falling to the oxygen-poor seabed as marine snow. If they're quickly buried, they may eventually form oil or gas. Land life, on the other hand, is more likely to form peat and eventually coal.

This paints a picture like this:

But hydrocarbon formation is a multi-step process[4]You can read more about it here. and lots of things can affect it. A huge amount of organic material washes into the ocean, and while most of it doesn't end up in oil-producing sediments, some of it does.[5]If you want to spend a day reading a bunch of articles on hydrocarbons and ocean sedimentation, you can check out a few here, here, here (paywall), here, and here. If you get tired halfway through, like I did, and want a change of pace, you can instead read an insane conspiracy theory website claiming that oil is not dead organic matter and that there's actually an infinite supply of it. This fact is apparently concealed from us by the New World Order and/or the Illuminati. Some oil fields—like Australia's—seem to have a lot of terrestrial sources. Most of this is plants, but some is certainly animals.[6]And it's worth noting that there were some aquatic dinosaurs—like Spinosaurus.

No matter where it came from, only a small fraction of the oil in your plastic dinosaur could be directly from real dinosaur corpses. If it came from a Mesozoic-era oil field fed heavily by land matter, it might contain a slightly larger share of dinosaurs; if it came from a pre-Mesozoic field sealed beneath caprock, it might contain no dinosaur at all. There's no way to know without painstakingly tracing every step of the manufacturing process of your particular toy.

In a broader sense, all water in the ocean has at some point been part of a dinosaur. When this water is used in photosynthesis, bits of it are used to build the fats and carbohydrates in the food chain—but a lot more of that water is in your body right now.

In other words, your plastic toys contain a lot less dinosaur than you do.

As a writer, I'm wondering what would be the cumulative energy of the hundreds of thousands of keystrokes required to write a novel.

—Nicolas Dickner

You probably shouldn't invest in a keyboard-based generator any time soon.

People like figuring out places where we can recover "wasted" energy. Avoiding waste is a great goal, but sometimes it's hard to judge how much energy is actually moving around in a particular system. Cool-sounding ideas like the recent "Solar Freaking Roadways" campaign don't always work out when you run the numbers. On the other hand, some clever ideas for collecting waste—like recovering the energy from doors opening or cars braking—turn out to be totally practical.

In the case of keyboards, there's a lot of engineering research into the force required to press keys, in part because so many people suffer from repetitive strain injuries. Using data from a study of rubber-dome keyboards—the most common type these days—we can estimate that the energy required to press a key is around 1.5 millijoules for a letter key and 2.5 for a big key like the enter key or spacebar.

How much is 1.5 millijoules? Well, it's enough to heat a drop of water by 1% of a degree. It's also enough to lift a squirrel 300 microns—all the way from the ground to the top of a stack of four sheets of paper!

Now that we know how much energy a keypress takes, we need to figure out how many keypresses are involved in writing a novel.

A typical novel might have half a million to a million characters in it,[1]Letters, I mean, although I can think of a book series which comes close on the other kind. so typing it out would require at least that many keypresses. The amount of backspacing and rewriting varies wildly from person to person. Some people write straight through without pausing, while others rewrite every sentence endlessly.

It turns out not to make a big difference which kind of writer you are. If you write straight through without editing, you'd expend about a kilojoule. With a lot of rewrites, you might expend several kilojoules—but you'd need to rewrite every word 10 times to match the energy stored in a single AA battery.

Writing one full novel would provide enough energy to run a laptop for a total of about 15 seconds. If each novel takes you six months, you'd spend one second out of every million running off keyboard power. This would save a fraction of a penny of electricity.

Now, a few novels every six months seems like a lot of typing, but plenty of people type more. The site WhatPulse offers tools to track mouse clicks and keystrokes, and hosts a community of users who post their statistics online and compete with each other to accumulate the highest total.

WhatPulse been running for more than a decade, and its oldest and the most active users have logged over 100 million keypresses. A heavy WhatPulse user types the equivalent of one novel every two months, and some of them manage one novel every few weeks.

However, that's still not fast enough to represent a lot of energy. To keep a laptop running from keypress power alone, you'd need to write a novel every ten seconds. To run a microwave would require one novel per second.[2]It would also require near-relativistic finger speeds, which would require impossible forces, huge amounts of extra energy for control, and would promptly destroy your hands AND the keyboard.

No matter how fast you type, writing isn't exercise.

What would happen if all the bodies of water on Earth magically disappeared?

—Joanna Xu

As is often the case with these questions, everyone would die.

The first people to notice would be swimmers and boaters, for obvious reasons.

To avoid a glass half empty scenario, we'll assume the water is replaced by air.

Most people swim in water which is relatively shallow, so most of them would survive the fall to the bottom, albeit with a few broken bones.[1]Those swimming in quarries and glacial lakes, on the other hand, could easily fall to their deaths a few feet from shore. People out on the ocean, on the other hand, would be in trouble.

The ones in shallow water would hit bottom first, since they wouldn't have as far to fall. Within the first second, a large fraction of the boats in lakes, rivers, and harbors would crash into the bottom, and many of those on board would survive.

Boats out on the ocean would take longer to fall. Over the next five seconds, a wave of crashes would spread outward from the continents, as boats struck the continental shelf farther and farther from shore. These boats would be smashed to tiny fragments, killing everyone on board.

After the first six or seven seconds, there would be a brief lull in the ship destruction rate. Continental shelves drop off steeply, and most of the ships out over the deep sea would take a little longer to fall.

The Titanic sank in about two miles of water. After it disappeared beneath the surface, the two halves of the ship took between 5 and 15 minutes to reach the bottom.[2]When the Titanic bow hit the sea floor, it was moving at almost exactly the same speed as when it struck the iceberg three hours earlier. (This is not quite a coincidence.) Without the ocean there, it would have reached the bottom in about 30 seconds, striking it at airliner cruising speed.[3]Although no one has ever dropped a cruise ship from a high altitude,^{[citation needed]} their terminal velocity at the surface is probably a little below the speed of sound. Because the air in the ocean basins would be compressed, the terminal velocity of ships near the bottom would be lower than at the surface. This compression also means that to magically replace the water, you'd need more air than you'd expect from the ocean's volume alone, since it would need a varying density profile. In other words, your water-replacement spells will need to have some calculations behind them.

Sufficiently advanced magic is indistinguishable from technology.

Within the first minute, just about every large ship would be on the bottom. The final boat to reach the bottom would probably be a small sailboat or life raft that was crossing an ocean trench when the water vanished. Thanks to low weight and/or drag from the sails, one of these vessels could take many minutes to reach the bottom.

If there were a seaplane floating on the deep ocean, it could conceivably survive, although it would take some luck and quick thinking by the pilot. The plane would initially drop, but as it gained speed it would tend to pull into a glide. After the initial shock, the pilot would have a reasonable amount of time to try to start the engine. Thanks in part to the thicker air, it's possible a seaplane could successfully land on a smooth patch of seabed. If the engine got started, the pilot could also try to fly to shore and land on a runway.

Fish, whales, and dolphins, and nearly all marine life would die immediately. Those near the bottom would suffocate or dessicate, while those near the surface in deeper water would suffer the same fate as boats.

Then the really weird stuff starts.

Without evaporation from lakes and oceans feeding the water cycle, it would stop raining. Without pools of water to drink from, people and most animals would dehydrate and die in a matter of days. Within a few weeks, plants would start withering in the ever-drier air. Within months, mass forest die-offs would begin.[4]Some drought-resistant trees could survive for years, but others wouldn't.

Huge amounts of dry, dead vegetation lead inevitably to fire, and within a few years, most of the world's forests would have burned. Forests store huge amounts of CO₂, and this burning would roughly double the amount of greenhouse gas in the atmosphere, accelerating global warming.

All in all, Joanna's scenario would result in virtually all life dying out pretty fast. But then things would get even worse.

Without a water cycle to weather rocks, the carbon-silicate feedback system which acts as a long-term thermostat to stabilize climate[5]CO₂ is added to the atmosphere by volcanoes (although at the moment, it's being added about ten times faster by people.) When water flows over certain rocks, chemical reactions suck CO₂ from the air and eventually bury it in seafloor sediments. With less CO₂, the planet gets colder. A colder planet means less evaporation, which means less weathering, which means CO₂ removal slows down. This feedback loop—which operates over much longer timescales than human-caused climate change—is probably what's kept the Earth's temperature relatively stable over the last few billion years (give or take a few snowball Earths) even though the Sun has gotten hotter. would shut down. Without this feedback, volcanic CO₂ would build up in our atmosphere, leading—in the long term—to scorching temperatures similar to what's happened on Venus.[6]Interestingly, because of Venus's lighter color (and thus higher reflectivity), it only absorbs about half the solar radiation that Earth does despite being substantially closer to the Sun. The thick blanket of CO₂ in its atmosphere is what keeps it hot.

We were going to lose our oceans anyway. As the Sun gets hotter, eventually water will start escaping through evaporation, and—one way or another—the planet will dry out and heat up. However, the loss of the oceans never seemed like something worth worrying too much about, since it's a billion years in the future. The oceans will be here long after our species is gone.

Unless Joanna ruins everything.

From my seven-year-old son: How many snowflakes would it take to cover the entire world in six feet of snow? (I don't know why six feet...but that's what he asked.)

—Jed Scott

It's been too hot where I live, so I like thinking about this question!

Snow is fluffy because it has a lot of air in it. The same amount of water that makes an inch of rain would make a lot more than an inch of snow.

An inch of rain is usually equal to about a foot of snow, but it depends on what kind of snow it is. If the snow is light and fluffy, an inch worth of rain could make over 20 inches of snow!

All the clouds in the world, combined, hold about 13 trillion tons of water. If all that water were spread out evenly and all fell at once, it would cover the Earth with an inch of rain—or a foot of snow.

Most of the Earth is ocean. If we only made water fall on land, there would be enough for three or four inches of water. That's how much falls in a very big rainstorm.

So three or four inches of water should add up to three or four feet of snow, right?

Almost, but there's a problem. When snow piles up, the snow on the bottom gets squished. If a foot of snow falls, then another foot falls, the snow on the bottom gets squished, which means the whole pile is shorter than two feet tall.

If you leave the snow there, it will slowly get less and less deep as it settles down and compacts. This means that even if six feet of snow fell everywhere, it would only be six feet at first. Before long, it might be five feet. (This happens to humans, too. You get shorter throughout the day as your body compresses a little!)

This can make it hard to record exactly how much snow falls, and sometimes even weather experts have a hard time! If you wait until the end of a snowstorm to measure snow, maybe it will have all squished down, or some of the snow might have melted, so your measurement will be too small.

Instead of waiting until the end of the storm, you can measure the snow in parts. You let some snow fall, measure it, then clear it away and wait for more snow to fall.

You have to decide how much snow to clear away. If wait too long, the snow might become too squished, but if you measure it too often, it will all be light and fluffy and you'll get a number that's way too high.

Believe it or not, the National Weather Service has written special guidelines for how often to clear away snow, so everyone can measure it the same way. They use a special snow-measuring board, which is probably just a regular piece of wood, but I like to imagine that they treat it like a precision instrument and store it in a special locked case until it's needed.

The official guidelines say that you should clear the snow-measuring board every six hours. A few years ago, there was a big snowstorm, and the Baltimore airport measured 28.6 inches of snow. That would have been a new record. But then the National Weather Service learned that the person measuring the snow had cleared the board every hour, instead of every six hours. So they didn't know whether to count the record or not.

I didn't see what they ended up deciding, because four days later, another blizzard hit Baltimore and everyone suddenly had more important things to worry about. (Then there were more after that one. It was a snowy winter.)

Still, people have never seen a winter with six feet of snow across the entire world. A snowfall like that would—to answer the original question—take a total of about a mole of snowflakes, give or take a few zeros. With that much snow, every one of the 70 million kids in the United States would be able to make enough snowballs to hit every other kid with a snowball three times over.

Or you could keep some of the snowballs for yourself. Right now, in the hot weather where I live, that sounds wonderful.

How long could the human race survive on only cannibalism?

Quinn Shaffer

There are about 500 trillion calories of human in the world. If it could be frozen or otherwise preserved, that would be enough—at least in terms of raw calories—to keep a tiny breeding population alive for millions of years.

Eating nothing but meat sounds bad, nutritionally, but the lack of vegetables wouldn't necessarily kill you. People can survive on high-meat or all-meat diets, especially if they eat things like organ meat and bone marrow; there are more vitamins and nutrients found in those which are missing from the narrower range of mammal skeletal muscle and fat in the typical western diet.

The US experienced meat shortages during World War II because so much food was being diverted to soldiers and allies overseas. In response to this, the US government decided to encourage Americans to eat more organs and other animal body parts. They employed some of the world's best anthropologists, psychologists, social scientists, and food scientists to figure out a way to change American eating habits.

One of the ideas the project had was that these foods should be rebranded as variety meats.[1]More on this in the hilarious Mary Roach book Gulp: Adventures on the Alimentary Canal A Google Books search shows the phrase appearing suddenly in US books around that time (a pattern not seen in British books.) When the war ended, many of these research efforts were dropped, but this 2002 article tries to piece together what they learned.

There are a lot of things we don't understand about nutritional deficiencies, and—to put it mildly—a lot of dispute over what kind of diets are healthy or aren't healthy. But no matter what nutrients we would or wouldn't get in Quinn's scenario, we'd face a bigger problem: contaminated food. Even if you cooked your meat, it would be hard to avoid all kinds of disease exposure as you worked your way through the remains of the human population.

In a small enough population, every outbreak is a pandemic; it wouldn't take long for something to wipe you out.

There are also some obvious practical problems. Unless you're one of a small handful of people, you have no way to kill the majority of living humans without some of them killing you first.

Let's consider a different scenario, one probably more in line with what Quinn was imagining: What if half the population ate the other half?[2]On second thought, I really have no idea what specific scenario Quinn was imagining, and I'm not sure I want to know.

If the average human weighs 50 kilograms and eats a couple thousand calories per day, then—according to Ryan North—then one person contains enough meat to feed another person for about a month.

If, every month, half the population eats the other half, we could go for 32 months[3]Which should make sense to the computer science students out there, since "7 billion" is just barely too big to store in a 32-bit integer. of cannibalism before the second-to-last person was eaten by the last.

Eating people who have eaten other people is a bad idea. For starters, it's a bad idea because you're eating people. Why are you eating people!? But it's also bad because it's an effective way to transmit prion diseases.

On the other hand, most prion diseases have lengthy incubation periods, so it might be a lesser concern in a world where you have a 50% chance of getting eaten every month.

Lastly, we'd have to decide who got eaten in which round. We could fight it out, or—to be fair—we could pair off and flip coins. If we did, the result would be, literally, ...

... the tournament bracket to end all tournament brackets.

Suppose you were to print, in 12 point text, the numeral 1 using a common cheap ink-jet printer. How many molecules of the ink would be used? At what numerical value would the number printed approximately equal the number of ink molecules used?

David Pelkey

This is the kind of problem where Fermi estimation comes in handy. In Fermi estimation, we're not concerned about exact numbers. We just want, before we start doing research, to get an idea of how big the number is going to be. Will it have 10 digits, or 100 digits, or a zillion?

We'll see what we can figure out before we look anything up.

An inkjet cartridge lets me print out some number of 8.5"x11" black-and-white pages. Let's be optimistic and say a few hundred. If each page has 500 words and each word has 5 letters, then each page has 2,500 letters. 100 pages is 250,000 letters and 400 would be 1,000,000. So the number of letters per cartridge probably has six digits.

Now, how many molecules are in an ink cartridge? This will be harder to estimate without cheating and looking things up, but let's try.

Let's say I remember hearing about "Avogadro's number" in chemistry class, but I don't remember exactly what it is. It's definitely something times 10²³, so it has 24 digits. And I remember that it's the number of atoms in some number of grams of something. It was a smallish number. Probably.[1]For the record, it's 6.022×10²³, and it's the number of carbon-12 atoms in 12 grams of carbon-12 (or the number of hydrogen atoms in a gram of hydrogen).

Inkjet cartriges probably also contain a small number of grams of ink.[2]Citation: If it were a big number, they would be hard to pick up, and if it were less than a gram, the idea that we've been paying $30 for them is just too upsetting to contemplate. Let's assume it's the same small number, because Fermi estimation lets us do that.

I have no idea what's in ink. (Remember, we're not allowed to look stuff up yet.) I know squid can make ink of some kind, so maybe ink has some big complicated organic molecules in it. That's bad, because I have no chance of estimating their weights to within even a few orders of magnitude.

Fortunately, what we need to worry the most about is the smallest molecules, because they'll contribute the most to the total count.

Ink probably has a lot of water in it, like many liquids. On the other hand, I bet most of those water molecules wander off when the ink dries—since that's what the word "dries" means.

We have nothing to go on here, so let's take a wild guess and suppose that a 10% of ink's bulk comes from large numbers of little molecules, ones comparable in size to the [mumble mumble carbon or something] atoms in Avogadro's number. Since Avogadro's number has 24 digits, 10% of it would be a 23-digit number. If our other guesses are right, then the number of molecules in an ink cartridge might also have about 23 digits

If there are a 23-digit number of molecules in an ink cartridge, and that cartridge prints a 6-digit number of letters, then each printed letter (or number) should contain a number of ink molecules with 23 - 6 = 17 digits.[3]What we're doing here is dividing by subtracting the number of digits. If you think this is a cool shortcut, and decide to develop it further and make it a little more rigorous and precise, then congratulations! You've just invented logarithms.

That means a printed 10-digit number contains about an 18-digit number of ink molecules, and a 100-digit number contains a 19-digit number of ink molecules. Aha! The crossover point, where the number of molecules and the printed number are equal, must happen somewhere between 18 and 19 digits.

So our answer, according to Fermi estimation, is in the neighborhood of a high 18-digit number. We might be off by several orders of magnitude in either direction, but in either case, it's definitely a number you could print out on a single line.

Now, let's do some actual research and find out how we did.

Inks, unsurprisingly, are complicated and vary a lot. Color inks contain a lot of large and heavy molecules, especially some of the pigments. Fortunately, cheap black inks—which are what David asked about—are simpler.

As our example, we'll take the ink used in the random HP printer at my house. HP doesn't disclose everything about what the ink is made of, but they do publish a material safety data sheet for it here.

The MSDS data tells us that the ink is over 70% water. It also contains the molecule 2-pyrrolidone (which is apparently used to synthesize the anti-seizure drug Ethosuximide) and 1,5-pentanediol.

In addition, it contains up to 5% "modified carbon black", a form of crystalline carbon (like graphite and diamond). This is great news for our estimate, because crystalline carbon is very simple; its molecular formula is just "C".[4]Assuming you count each carbon atom separately. You could interpret David's question to mean particles of ink, so each hunk of carbon black would only count as 1. However, that would mean working out exactly what water fraction remains in the dried ink and how much weight 1,5-pentanediol contributes and so forth, and that sounds like more work.

Conveniently, "C" is also what's used in the definition of Avogadro's number. Small consumer cartridges contain a few grams of ink, which is less than the 12 grams used in Avogadro's number. That might make our estimate about half a digit too high. And while we were lucky at guessing carbon, HP ink contains less than 5% carbon black, not the 10% we guessed. That pushes the real answer down even lower than our estimate. But all in all, we did pretty well!

Of course, this is a reminder of how much easier the digital world is:

It's also a reminder of how expensive ink is. Speaking of which, the ink sac from the tiny Octopoteuthis deletron squid are probably a few milliliters, based on the collection bottle sizes mentioned in this paper, for a squid that probably only weighs a hundred grams or so.

$30 could probably get you a few kilograms of fresh whole squid, and—if you picked the right squid—a total of five or six cartridges worth of ink.

Lifehacks.

What’s the fastest way to get a hand-written letter from my place in Chicago to my mother in New Jersey?

—Tim

First, let's carefully consider the "walking" option. Who knows—maybe it's faster than it seems!

Since you didn't specify where in New Jersey your mother lives, I'm going to assume she's in Hackensack, because that's where Miss Teschmacher's mother lived.[1]You know, Superman falls into the pool almost headfirst. Why would Lex Luthor assume the necklace would stay on him in the water? This always bothered me. The rest of the movie is totally legit; this is the only thing that seems unrealistic.

Google Maps says that it would take 260 hours, or just under 11 days, to walk from Chicago to Hackensack.

Google takes you on an interesting route. For example, it cuts diagonally across farmer's fields, which seems strange, until you realize it's taking you along the Wabash Cannonball Trail, a 63-mile walking path that follows an old rail line. Clever!

On the other hand, Google makes some questionable decisions. When you get to Mifflinburg, Pennsylvania, Google has you walk down Old Turnpike Road to reach Lewisburg. This is strange, because[2]... as any schoolchild knows ... the Buffalo Valley trail runs right alongside the highway for this entire stretch, just a few hundred yards to the north of the road. But who knows—maybe Google has some secret reason for steering you away from what would otherwise be a perfect walking path.

Your trip would also take you past that really weird bend in the Appalachians. Many years ago, I took my first flight across Pennsylvania, and I was totally baffled when I looked out the window and saw strange curving troughs running across the landscape. They were so smooth and regular that at first I thought they must be manmade, but they were too big and endless for that. What I was seeing was the curved troughs of the Ridge and Valley Appalachians, which curve dramatically across Pennsylvania.[3]Just a few weeks ago, researchers finally explained how that weird bend formed.

While the 10-day walk would be scenic, it's not looking like the fastest method. We'll need to try something else.

If it were 1861, you could use the Pony Express, which could move a letter over that distance in as little as 3 days.

Since it's no longer 1861,^{[citation needed]} we have better options available. FedEx offers overnight delivery, and a courier service could make the drive in a little over 12 hours.

Last year, Ed Boilan absolutely shattered the "cannonball run" record for driving from New York to Los Angeles—and broke laws in hundreds of jurisdictions in the process. His average speed was 98 mph, and while it's safe to assume he probably averaged less than this across the eastern half of his journey, if you managed to keep up his 98 mph average across your trip, you could make it from Chicago to Hackensack in 8 hours.

Airplanes are a lot faster. An airliner can cover the distance in an hour and a half, and the Concorde—back when it was still flying—could do it in 30 minutes (plus some time to take off and land).

There are other techniques, like using a rail gun to fire a message capsule down a vacuum tube, which could conceivably get your time down to 10 or 20 minutes.

But none of these beat missiles.

Over a short flight distance, an ICBM[4]In this case, an intracontinental ballistic missile. on a typical arc would take about 12 to 15 minutes to cover the distance to your mom.[5]This is probably the first time I've ever ended a sentence with those words when I wasn't making a "your mom" joke. But using depressed trajectories, a technique which should make sense to the Kerbal Space Program players out there, the time to cross the distance between you and your mother could be reduced to as little as six minutes. Of course, the letter might not be readable once the maneuver is completed, but that's ok—your mother will probably no longer be capable of reading it.

In the end, when it comes to getting a physical object to Hackensack, New Jersey as fast as possible, Lex Luthor had the right idea.

Even if not everything he said made sense.

What would be the most expensive way to fill a size 11 shoebox (e.g. with 64 GB MicroSD cards all full of legally purchased music)?

Rick Lewis

A shoebox full of valuable stuff seems to top out at about $2 billion. Surprisingly, this turns out to be true for a wide range of possible fillings.

The MicroSD cards are a good idea. iTunes songs cost about $1 each, and MicroSD cards have a capacity of about 1.6 petabytes per gallon. A men's size 11 shoebox is about 10-15 liters, depending on the brand and type of shoe, which means it can hold up to 1.5 billion 4 MB songs (at about a dollar each). (That's about 20 times as many songs as the iTunes store offers, so you'll have to buy some of the songs more than once.)

Expensive software like Adobe®©™ Photoshop®©™ CS®™ 5™ has a slightly higher cost-to-megabyte ratio, since it retails for several hundred dollars and takes up several hundred megabytes of space. Or, at least, it used to, until Adobe moved to a cloud model.

Once you start considering software prices, you can probably crank the "cost" of things in a shoebox as high as you want by making unlimited in-app purchases. And while the resulting RPG character may technically represent the result of your spending that much money, it's hard to argue with a straight face that your character is in any sense worth a trillion dollars.

So let's think about actual objects.

There's gold, of course. 13 liters of gold is worth about $10 million as of this writing. Platinum is a little more expensive at $13 million/shoebox.[1]Not yet an SI unit, sadly. That's about 10 times the value of a shoebox full of $100 bills. On the other hand, a shoebox full of gold would weigh as much as a small horse.

There are more expensive metals. A gram of pure plutonium, for example, would cost about $5k. As a bonus, plutonium is even denser than gold, which means you could fit almost 300 kilograms of it in a shoebox.

Before you spend $3 billion on plutonium, take note: Plutonium's critical mass is about 10 kilograms. So while you could fit 300 kilograms of it in a shoebox, you could only do so briefly.

High-quality diamonds are expensive, but it's hard to get a handle on their exact price because the entire industry was built on a scam the gemstone market is complicated. One site quotes a price of over \$300,000 for a flawless 600 mg (3 carat) diamond—which means that a shoebox full of perfect-quality gem diamonds could be worth as much as \$20 billion—but \$1 or \$2 billion is more reasonable.

Many illegal drugs are, by weight, more valuable than gold. Cocaine's price varies a lot, but in many areas is in the neighborhood of $100/gram.[2]My search history after researching drug street prices would probably get me on all kinds of government watch lists, if I weren't on them all already for all the other things I've researched for this blog. Gold is currently less than half that. However, cocaine is much less dense than gold,[3]But wait—what is the density of cocaine? As usual, the Straight Dope Message Board folks are on the case; in this discussion, they consult the CRC Handbook and Merck Index, before giving up and deciding that it's probably about 1 kg/L, like most organic substances. They do, however, learn its boiling point and solubility in olive oil. so a shoebox full of cocaine would be less valuable than one of gold.

Cocaine is not the most expensive drug by weight. LSD—probably the most widely-consumed substance sold to consumers by the microgram—costs about a thousand times more than cocaine by weight. A shoebox full of pure LSD would be worth about $2.5 billion.

Some prescription drugs can be just as expensive as LSD. A single dose of brentuximab vedotin (Adcetris) can cost \$13,500, which—for the average patient—puts its shoebox value in the same \$2 billion range as LSD, plutonium, and MicroSD cards. Other drugs are even more expensive.

Of course, you could always put shoes in the shoebox.

Judy Garland's shoes from The Wizard of Oz sold at auction for $666,000, and—unlike the other things we've considered—may have, at one point, actually been placed in a shoebox.

If you really want to fill a shoebox with an arbitrarily large amount of money, you could get the US Treasury to mint you a trillion-dollar platinum coin.

But if you're open to leveraging our monetary system's legal authority to impart value into an arbitrary inanimate object ...

... you could just write a check.