How long would it take for people to notice their weight gain if the mean radius of the world expanded by 1cm every second? (Assuming the average composition of rock were maintained.)

Dennis O'Donnell

The Earth is not, currently, expanding.<sup>[Yes, I have a citation for this.

"In conclusion, no statistically significant present expansion rate is detected by our study within the current measurement uncertainty of 0.2 mm yr−1."

Wu, X., X. Collilieux, Z. Altamimi, B. L. A. Vermeersen, R. S. Gross, and I. Fukumori (2011), Accuracy of the International Terrestrial Reference Frame origin and Earth expansion, Geophys. Res. Lett., 38, L13304, doi:10.1029/2011GL047450.]</sup>

People have long suggested that it might be. Before the continential drift hypothesis was confirmed in the 1960s,^{[The smoking gun that confirmed the plate tectonics hypothesis was the discovery of seafloor spreading. The way seafloor spreading and magnetic pole reversal neatly confirmed each other is one of my favorite examples of scientific discovery at work.]} people had noticed that the continents fit together. Various ideas were put forward to explain this, including the idea that the ocean basins were rifts that opened in the surface of a previously-smooth Earth as it expanded. This theory was never very widespread,^{[It turns out it's kind of dumb.]} although it still periodically makes the rounds on YouTube.

To avoid the problem of rifts in the ground, let's imagine all the matter in the Earth, from the crust to the core, starts expanding uniformly. To avoid another Drain the Oceans scenario, we'll assume the ocean expands, too.^{[As it turns out, the ocean is expanding, since it's getting warmer. This is (currently) the main way global warming is raising the sea level.]} All human structures will stay.

t = 1 second:

Oh, ok.

As the Earth started expanding, you'd feel a slight jolt, and might even lose your balance for a moment. This would be very brief. Since you're moving steadily upward at 1 cm/s, you woudn't feel any kind of ongoing acceleration. For the rest of the day, you wouldn't notice much of anything.

t = 1 day:

After the first day, the Earth would have expanded by 864 meters.

Let's go ride bikes!

Gravity would take a long time to increase. If you weighed 70 kilograms when the expansion started, you'd weigh 70.01 at the end of the day.

What about our roads and bridges? Eventually, they would have to break up, right?

Not as quickly as you might think. Here's a puzzle I once heard:

Imagine you tied a rope tightly around the Earth, so it was hugging the surface all the way around.

This diagram taken from some ambitious Ikea assembly instructions.

Now imagine you wanted to raise the rope one meter off the ground.

This chair doesn't look right.

How much extra length will you need to add to the rope?

Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase radius by 1 unit, you increase circumference by 2π units.

Stretching a 40,000-kilometer line an extra 6.28 meters is pretty negligible. Even after a day, the extra 5.4 kilometers would be handled easily by virtually all structures. Concrete expands and contracts by more than that every day.^{[Lawrence Grybosky, Thermal Expansion and Contraction]}

After the initial jolt, one of the first effects you'd notice would be that your GPS would stop working. The satellites would stay in roughly the same orbits, but the delicate timing that the GPS system is based on would be completely ruined within hours. GPS timing is incredibly precise; of all the problems in engineering, it's one of the only ones in which engineers have been forced to include both special and general relativity in their calculations.

Most other clocks would keep working fine. However, if you have a very precise pendulum clock, you might notice something odd—by the end of the day, it would be three seconds ahead of where it should be.

t = 1 month:

After a month, the Earth would have expanded by 26 kilometers—an increase of 0.4%—and its mass would have increased by 1.2%. Surface gravity would only have gone up by 0.4%, rather than 1.2%, since surface gravity is proportional to radius.^{[Mass is proportional to radius cubed, and gravity is proportional to mass times inverse square of radius, so radius3 / radius2 = radius.]}

You might notice the difference in weight on a scale, but it's not a big deal. Gravity varies by this much between different cities already. This is a good thing to keep in mind if you buy a digital scale. If your scale has a precision of more than two decimal places, you need to calibrate it with a test weight—the force of gravity at the scale factory isn't necessarily the same as the force of gravity at your house.

While you might not notice the increased gravity just yet, you'd notice the expansion. After a month, you'd see a lot of cracks opening up in long concrete structures and the failure of elevated roads and old bridges. Most buildings would probably be ok, although those anchored firmly into bedrock might start to behave unpredictably.^{[Just what you want in a skyscraper.]}

At this point, astronauts on the ISS would start getting worried. Not only would the ground (and atmosphere) be rising toward them, but the increased gravity would also cause their orbit to slowly shrink. They'd need to evacuate quickly; they'd have at most a few months before the station reentered the atmosphere and deorbited.

t = 1 year:

After a year, gravity would be 5% stronger. You'd probably notice the weight gain, and you'd definitely notice the failure of roads, bridges, power lines, satellites, and undersea cables. Your pendulum clock would now be ahead by five days.

What about the atmosphere?

If the atmosphere isn't growing like the land and water are, air pressure would start dropping. This is due to a combination of factors. As gravity increases, then air gets heavier. But since that air is spread out over a larger area, the overall effect would be decreasing air pressure.

On the other hand, if the atmosphere is also expanding, surface air pressure would rise. After years had passed, the top of Mt. Everest would no longer be in the "death zone".^{[See What-If #64.]} On the other hand, since you'd be heavier—and the mountain would be taller—climbing would be more work.

t = 5 years:

After five years, gravity would be 25% stronger. If you weighed 70 kg when the expansion started, you'd weigh 88 kg now.

Most of our infrastructure would have collapsed. The cause of the collapse would be the expanding ground below them, not the increased gravity. Surprisingly, most skyscrapers would hold up fine under much higher gravity.^{[Although I wouldn't trust the elevators.]} For most of them, the limiting factor isn't weight, but wind.

t = 10 years:

After 10 years, gravity would be 50% stronger. In the scenario where the atmosphere isn't expanding, the air would become thin enough to be difficult to breathe even at sea level. In the other scenario, we'd be ok for a little while longer.

t = 40 years:

After 40 years, Earth's surface gravity would have tripled.^{[Over decades, the force of gravity would grow slightly faster than you'd expect, since the material in the Earth would compress under its own weight. The pressure inside planets is roughly proportional to the square of their surface area, so the Earth's core would be squeezed tightly.]} At this point, even the strongest humans would only be able to walk with great difficulty. Breathing would be difficult. Trees would collapse. Crops wouldn't stand up under their own weight. Virtually every mountainside would see massive landslides as material sought out a shallower angle of repose.

Geologic activity would also accelerate. Most of the Earth's heat is provided by radioactive decay of minerals in the crust and mantle,^{[Although some radioactive elements, like uranium, are heavy, they get squeezed out of the lower layers because their atoms don't mesh well with the rock lattices at those depths. For more, see this chapter and this article.]} and more Earth means more heat. Since the volume expands faster than the surface area, the overall heat flowing out per square meter will increase.

It's not actually enough to substantially warm the planet—Earth's surface temperature is dominated by the atmosphere and the Sun—but it would lead to more volcanoes, more earthquakes, and faster tectonic movement. This would be similar to the situation on Earth billions of years ago, when we had more radioactive material and thus a hotter mantle.

More active plate tectonics might be good for life. Plate tectonics play a key role in stabilizing the Earth's climate, and planets smaller than Earth (like Mars) don't have enough internal heat to sustain long-term geologic activity. A larger planet would allow for more geologic activity, which is why some scientists think that exoplanets slightly larger than Earth ("super-Earths") could be more friendly to life than Earth-sized ones.^{[Sasselov, Dimitar D.. The life of super-Earths: how the hunt for alien worlds and artificial cells will revolutionize life on our planet. New York: Basic Books, 2012.]}

t = 100 years:

After 100 years, we'd be experiencing over six gees of gravity. Not only would we be unable to move around to find food, but our hearts would be unable to pump blood to our brains. Only small insects (and sea animals) would be physically able to move around. Perhaps humans could survive in specially-built controlled-pressure domes, moving around by keeping most of our bodies submerged in water.

Early scientists believed, based on the fossil record, that humans must be aquatic; it would be the only way they could have supported their weight against gravity.

Breathing in this situation would be difficult. It's hard to suck in air against the weight of the water, which is why snorkels can only work when your lungs are near the surface.

Outside of low-pressure domes, the air would become unbreathable for a different reason. At somewhere around 6 atmospheres, even ordinary air becomes toxic.^{[R.M. Franz and P.C. Schutte, Barometric hazards within the context of deep-level mining, The Journal of The South African Institute of Mining and Metallurgy]} Even if we'd managed to survive all the other problems, by 100 years, we'd be dead from oxygen toxicity. Toxicity aside, breathing dense air is difficult simply because it's heavy.

Black hole?

When would the Earth eventually become a black hole?

It's hard to answer that, because the premise of the question is that the radius is steadily expanding while the density stays the same—whereas a black hole, the density increases.

The dynamics of really huge rocky planets aren't often analyzed, since there's no obvious way that they could form; anything that large will have enough gravity to gather hydrogen and helium during planet formation and become a gas giant.

At some point, our growing Earth would reach the point where adding more mass causes it to contract, rather than expand. After this point, it would collapse into something like a sputtering white dwarf or neutron star, and then—if its mass kept increasing—eventually become a black hole.

But before it gets that far ...

t = 300 years:

It's a shame humans wouldn't live this long, because at this point, something really neat would happen.

As the Earth grows, the Moon would, like all our satellites, gradually spiral inward.^{[Plummer, H. C., Note on the motion about an attracting centre of slowly increasing mass, Monthly Notices of the Royal Astronomical Society, Vol. 66, p.83]} After several centuries, it would be close enough to the swollen Earth that the tidal forces between Earth and the Moon would be stronger than the gravitational forces holding the Moon together.

When the Moon passed this boundary—called the Roche limit—it would gradually break apart ...

If you liked it then you should have moved a mass inside its Roche limit.

... and Earth would, for a short time, have rings.

you became my giant lizard

Little Planet

If an asteroid was very small but supermassive, could you really live on it like the Little Prince?

Samantha Harper

Last week, we looked at at life on a giant world. This week, let's look at a small one.

'Did you eat my rose?' 'Maybe.'

The Little Prince, by Antoine de Saint-Exupéry, is a story about a traveler from a distant asteroid. It's simple and sad and poignant and memorable.^{[For another take on the Petit Prince, scroll down to the last section of this wonderful piece by Mallory Ortberg.]} It's ostensibly a children's book, but it's hard to pin down who the intended audience is. In any case, it certainly has found an audience; it's among the best-selling books in history.

Personally, I always thought it looked like a snake that had swallowed a hat.

It was written in 1942. That's an interesting time to write about asteroids, because in 1942 we didn't actually know what asteroids looked like. Even in our best telescopes, the largest asteroids were only visible as points of light. In fact, that's where their name comes from—the word asteroid means "star-like."

We got our first confirmation of what asteroids looked like in 1971, when Mariner 9 visited Mars and snapped pictures of Phobos and Deimos.^{[Here's a picture of Phobos looking like the archetypical asteroid. The archived images from the mission are at the NASA Space Science Data Center, but strangely, the NSSDC refers readers to someone's personal Tripod page to browse the actual images.]} These moons, believed to be captured asteroids,^{[Ironically, while Phobos and Deimos look like asteroids, new research suggests they're not. See Craddock, Robert A.. "Are Phobos And Deimos The Result Of A Giant Impact?". Icarus (2010)]} solidified the modern image of asteroids as cratered potatoes.

A potato.

Before the 1970s, it was common for science fiction to assume small asteroids would be round, like planets.^{[Not always; plenty of people had a good idea of what they would look like. And there were stranger ideas ...]}

The Little Prince took this a step further, imagining an asteroid as a tiny planet with gravity, air, and a rose. There's no point in trying to critique the science here, because (1) it's not a story about asteroids, and (2) it opens with a parable about how foolish adults are for looking at everything too literally.

So rather than trying to take things away from the story, let's see what strange new pieces science can add. If there really were a superdense asteroid with enough surface gravity to walk around on, it would have some pretty surprising properties.

If the asteroid has a radius of 1.75 meters, then in order to have Earth-like gravity at the surface, it would need to have a mass of about 500 million tons. This is roughly equal to the combined mass of every human on Earth.

If you stood on the surface, you'd experience tidal forces. Your feet would feel heavier than your head, which you'd feel as a gentle stretching sensation. It would feel like you were stretched out on a curved rubber ball, or were lying on a merry-go-round with your head near the center.

My back hasn't felt this good in years.

The escape velocity at the surface would be about 5 meters per second. That's slower than a sprint, but still pretty fast. As a rule of thumb, if you can't dunk a basketball, you wouldn't be able to escape by jumping straight up.

I believe I can flyyyy

However, the weird thing about escape velocity is that it doesn't matter which direction you're going.^{[... which is why it should really be called "escape speed"—the fact that it has no direction (which is the distinction between "speed" and "velocity") is actually very significant here.]} If you go faster than the escape speed, as long as you don't actually go toward the planet, you'll escape. That means you might be able to leave our asteroid by running horizontally and jumping off the end of a ramp.

Wheeeeeeeeeeeeeee

If you didn't go fast enough to escape the planet, you'd go into orbit around it. Your orbital speed would be roughly 3 meters per second, which is a typical jogging speed.

Those ants down below look like people.

But this would be a weird orbit.

Tidal forces would act on you in several ways. If you reach your arm down toward the planet, it would be pulled much harder than the rest of you. And if you reach down with one arm, the rest of you gets pushed upward, which means other parts of your body feel even less gravity. Effectively, every part of your body would be trying to go in a different orbit.

A large orbiting object under these kinds of tidal forces—say, a moon—will generally break apart into rings. This wouldn't happen to you. However, your orbit would become chaotic and unstable.

These types of orbits were investigated in an interesting paper by Radu D. Rugescu and Daniele Mortari.^{[Rugescu, Radu D., Mortari, Daniele, "Ultra Long Orbital Tethers Behave Highly Non-Keplerian and Unstable", WSEAS Transactions on Mathematics, Vol. 7, No. 3, March 2008, pp. 87-94.]} Their simulations showed that large, elongated objects follow strange patterns around their central bodies. Even their centers of mass don't move in the traditional ellipses; some adopt pentagonal orbits, while others spin chaotically and crash into the planet.

This is KSP on nightmare mode.

This type of analysis could actually have practical applications. There have been various proposals over the years to use long, whirling tethers to move cargo in and out of gravity wells—a sort of free-floating space elevator. Such tethers could transport cargo to and from the surface of the Moon, or to pick up spacecraft from the edge of the Earth's atmosphere. The inherent instability of many tether orbits poses an interesting challenge for this kind of project.

As for the residents of our superdense asteroid, they'd have to be careful; if they ran too fast, they'd be in serious danger of going into a tumble and losing their lunch.

Fortunately, vertical jumps would be fine.

Cleveland-area fans of French children's literature were disappointed by his decision to sign with the Miami Heat.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Facebook of the Dead

When, if ever, will Facebook contain more profiles of dead people than of living ones?

Emily Dunham

Either the 2060s or the 2130s.

'Put on your headphones!' 'Can't. Ears fell off.'

There are not a lot of dead people on Facebook. The main reasons for this is that Facebook—and its users—are young. The average Facebook user has gotten older over the last few years, but the site is still used at a much higher rate by the young than by the old.^{[There are a zillion surveys confirming this, such as this one from eMarketer.]}

The Past:

Based on the site's growth rate, and the age breakdown of their users over time,^{[You can get user counts for each age group from Facebook's create-an-ad tool, although you may want to try to account for the fact that Facebook's age limits cause some people to lie about their ages.]} there are probably 10 to 20 million people who created Facebook profiles who have since died.

These people are, at the moment, spread out pretty evenly across the age spectrum. Young people have a much lower death rate than people in their sixties or seventies, but they make up a substantial share of the dead on Facebook simply because there have been so many of them using it.

The Future:

About 290,000 US Facebook users will die (or have died) in 2013. The worldwide total for 2013 is likely several million.^{[Note: In some of these projections, I used US age/usage data extrapolated to the Facebook userbase as a whole, because it's easier to find US census and actuarial numbers than to assemble the country-by-country for the whole Facebook-using world. The US isn't a perfect model of the world, but the basic dynamics—young people's Facebook adoption determines the site's success or failure while population growth continues for a while and then levels off—will probably hold approximately true. If we assume a rapid Facebook saturation in the developing world, which currently has a faster-growing and younger population, it shifts many of the landmarks by a handful of years, but doesn't change the overall picture as much as you might expect.]} In just seven years, this death rate will double, and in seven more years it will double again.

Even if Facebook closes registration tomorrow, the number of deaths per year will continue to grow for many decades, as the generation who was in college between 2000 and 2020 grows old.

An elderly Cory Doctorow cosplaying by wearing what the future thinks he wore in the past.

The deciding factor in when the dead will outnumber the living is whether Facebook adds new living users—ideally, young ones—fast enough to outrun this tide of death for a while.

Facebook 2100:

This brings us to the question of Facebook's future.

We don't have enough experience with social networks to say with any kind of certainty how long Facebook will last. Most websites have flared up and then gradually declined in popularity, so it's reasonable to assume Facebook will follow that pattern.^{[I'm assuming, in these cases, that no data is ever deleted. So far, that's been a reasonable assumption; if you've made a Facebook profile, that data probably still exists, and most people who stop using a service don't bother to delete their profile. If that behavior changes, or if Facebook performs a mass purging of their archives, the balance could change rapidly and unpredictably.]}

In that scenario, where Facebook starts losing market share later this decade and never recovers, Facebook's crossover date—the date when the dead outnumber the living—will come sometime around 2065.

But maybe it won't. Maybe it will take on a role like the TCP protocol, where it becomes a piece of infrastructure on which other things are built, and has the inertia of consensus.

If Facebook is with us for generations, then the crossover date could be as late as the mid-2100s.

That seems unlikely. Nothing lasts forever, and rapid change has been the norm for anything built on computer technology. The ground is littered with the bones of websites and technologies that seemed like permanent institutions ten years ago.

It's possible the reality could be somewhere in between.^{[Of course, if there's a sudden rapid increase in the death rate of Facebook users—possibly one that includes humans in general—the crossover could happen tomorrow.]} We'll just have to wait and find out.

The fate of our accounts:

Facebook can afford to keep all our pages and data indefinitely. Living users will always generate more data than dead ones, and the accounts for active users are the ones that will need to be easily accessible. Even if accounts for dead (or inactive) people make up a majority of their users, it will probably never add up to a large part of their overall infrastructure budget.

More important will be our decisions. What do we want for those pages? Unless we demand that Facebook deletes them, they will presumably, by default, keep copies of everything forever. Even if they don't, other data-vacuuming organizations will.

Right now, next-of-kin can convert a dead person's Facebook profile into a memorial page. But there are a lot of questions surrounding passwords and access to private data that we haven't yet developed social norms for. Should accounts remain accessible? What should be made private? Should next-of-kin have the right to access email? Should memorial pages have comments? How do we handle trolling and vandalism? Should people be allowed to interact with dead user accounts? What lists of friends should they show up on?

These are issues that we're currently in the process of sorting out by trial and error. Death has always been a big, difficult, and emotionally charged subject, and every society finds different ways to handle it.

The basic pieces that make up a human life don't change. We've always eaten, learned, grown, fallen in love, fought, and died. In every place, culture, and technological landscape, we develop a different set of behaviors around these same activites.

Like every group that came before us, we're learning how to play those same games on our particular playing field. We're developing, through sometimes messy trial and error, a new set of social norms for dating, arguing, learning, and growing on the internet. Sooner or later, we'll figure out how to mourn.

★★☆☆☆

Happy Halloween!

with the van, we went around in the cold, always dreaming of a better place and hugging hot at night

The Constant Groundskeeper

How big of a lawn would you have to have so that when you finished mowing you'd need to start over because the grass has grown?

Nick Nelson

According to the Turfgrass Extension and Outreach program at UIUC,^{[The Morrow cornfields operated by the university are the most valuable cornfields in the world, and part of one of the world's longest-running scientific experiments.]} every mowing should remove one third of the grass blade's height.

The UIUC Turfgrass 2013 Battle Plan, I hope.

Grass grows slower or faster depending on the weather, but we'll assume an average growth rate of 0.2 inches per day. This figure comes from Mowing Your Lawn, a document published by by Iowa State's Yard and Garden Extension program (which, I like to imagine, has a vicious and occasionally bloody rivalry with the UIUC Turfgrass crew).

A typical pushmower at a fast walking speed can mow a little under a square meter per second. If you mowed without stopping from 8:00 AM to 6:00 PM, you would cover about 25,000 square meters.^{[or 6 acres, or 2.5 hectares, or 7,500 square fathoms, or 8,500 square smoots, or 5,300 Shrouds of Turin]} To maintain your lawn at a height of four inches, you would need to mow it every ten days. If you mowed more or less frequently, you could risk damaging the lawn—or, worse, incur the wrath of UIUC.

At ten hours of mowing per day, you could cover a quarter of a square kilometer before you'd have to circle back to the beginning and start over. If the entire area of Vatican City, indoors and out, were covered in perennial ryegrass,^{[Perhaps due to an ill-advised UIUC undergraduate project]} you would be able to keep about half of it neatly trimmed.

With the help of Pope Emeritus Benedict, they could cover the whole thing!

You could improve on this with a larger, faster mower. An oversized rider mower at 12 miles per hour^{[The maximum listed in the Cub Cadet rider mower acres-per-hour chart ]} could mow as much as two square kilometers, which Wolfram|Alpha helpfully tells me is 0.5% to 1% of an adult male cougar's home range.

A cougar chasing down a deere.

In 2010, Bobby Cleveland set a world record for the top speed in a riding lawnmower, hitting 96 mph. This record was set as part of a rivalry with the British lawnmower driver Don Wales.^[Really.]

In a blow to its national pride, the US has lost that record. Sometime in the last few years, the magazine Top Gear commissioned Honda to build them an even faster lawnmower. A few months ago, this mower—which shoots flames from the exhaust pipe—broke 100 mph on a test track in France.^{["First tests of '130mph' lawnmower", BBC News Technology, 17 July 2013]} The builders claim it will eventually reach 130 mph. The mower is still capable of cutting grass (using a custom wire mechanism), but when running at top speed the trimmer is removed for safety reasons.

With the Top Gear mower, what's the maximum area we could cut?

Let's set safety aside and assume we can leave the mower's cutting mechanism in place. Let's also assume that the mower can cut a strip two meters wide while running at top speed.

Under those assumptions, if the mower is run for 24 hours a day, seven days a week ...

Since cougars aren't found in Europe, perhaps 'top speed by a rider mower carrying a cougar' is a record that Americans can more reliably dominate.

... it could just about keep one adult male cougar's home range neatly trimmed.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Stirring Tea

I was absentmindedly stirring a cup of hot tea, when I got to thinking, "aren't I actually adding kinetic energy into this cup?" I know that stirring does help to cool down the tea, but what if I were to stir it faster? Would I be able to boil a cup of water by stirring?

Will Evans

No.

The basic idea makes sense. Temperature is just kinetic energy. When you stir tea, you're adding kinetic energy to it, and that energy goes somewhere. Since the tea doesn't do anything dramatic like rise into the air or emit light, the energy must be turning to heat.

Am I making tea wrong?

The reason you don't notice the heat is that you're not adding very much of it. It takes a huge amount of energy to heat water; by volume, it has a greater heat capacity than any other common substance.^{[Hydrogen and helium have a higher heat capacity by mass, but they're diffuse gasses. The only other common substance with a higher heat capacity by mass is ammonia. All three of these lose to water when measured by volume.]}

If you want to heat water from room temperature to nearly boiling in two minutes, you'll need a lot of power:

(Note: Pushing almost-boiling water to boiling takes a large burst of extra energy on top of what's required to heat it to the boiling point—this is called the enthalpy of vaporization.)

Our formula tells us that if we want to make a cup of hot water in two minutes, we'll need a 700-watt power source. A typical microwave uses 700 to 1100 watts, and it takes about two minutes to heat a mug of water to make tea. It's nice when things work out!^{[If they didn't, we'd just blame "inefficiency" or "vortices".]}

700 watts for two minutes is an awful lot of energy. When water falls from the top of Niagara Falls, it gains kinetic energy, which is converted to heat at the bottom. But even after falling that great distance, the water only heats up by a fraction of a degree.^[] To boil a cup of water, you'd have to drop it from higher than the top of the atmosphere.

(The British Felix Baumgartner)

How does stirring compare to microwaving?

Based on figures from industrial mixer engineering reports,^{[Brawn Mixer, Inc., Principles of Fluid Mixing (2003)]} I estimate that vigorously stirring a cup of tea adds heat at a rate of about a ten-millionth of a watt. That's completely negligible.^{[Tea loses heat a much higher rate than this. See: Ben Harden, Tea temperature vs. Time graph]}

The physical effect of stirring is actually a little complicated.<sup>[In some situations, mixing liquids can actually help keep them warm. Hot water rises, and when a body of water is large and still enough (like the ocean) a warm layer forms on the surface. This warm layer radiates heat much more quickly than a cold layer would. If you disrupt this hot layer by mixing the water, the rate of heat loss decreases.

This is why hurricanes tend to lose strength if they stop moving forward—their waves churn up cold water from the depths, cutting them off from the thin layer of hot surface water that was their main source of energy.]</sup> Most of the heat is carried away from teacups by the air convecting over them, and so they cool from the top down. Stirring brings fresh hot water from the depths, so it can help this process. But there are other things going on—stirring disturbs the air, and it heats the walls of the mug. It's hard to be sure what's really going on without data.

Fortunately, we have the internet. StackExchange user drhodes measured the rate of teacup cooling from stirring vs. not stirring vs. repeatedly dipping a spoon into the cup vs. lifting it. Helpfully, drhodes posted both high-resolution graphs and the raw data itself, which is more than you can say for a lot of journal articles.

The conclusion: It doesn't really matter whether you stir, dip, or do nothing; the tea cools at about the same rate (although dipping the spoon in and out of the tea cooled it slightly faster).

Which brings us back to the original question: Could you boil tea if you just stirred it hard enough?

No.

The first problem is power. 700 watts is about a horsepower, so if you want to boil tea in two minutes, you'll need at least one horse to stir it hard enough.

But I can't understand the microwave buttons because they're confusing and I'm a horse.

You can reduce the power requirement by heating the tea over a longer period of time, but if you reduce it too far the tea will be cooling as fast as you're heating it.

Even if you could churn the spoon hard enough—tens of thousands of stirs per second—fluid dynamics would get in the way. At those high speeds, the tea would cavitate; a vacuum would form along the path of the spoon and stirring would become ineffective.

And if you stir hard enough that your tea cavitates, its surface area will increase very rapidly, and it will cool to room temperature in seconds:

At least the teacup wasn't half empty.

No matter how hard you stir your tea, it's not going to get any warmer.

everything we want is possible, that's how well we work

Loneliest Human

What is the furthest one human being has ever been from every other living person? Were they lonely?

Bryan J. McCarter

It's hard to know for sure!

The most likely suspects are the six Apollo command module pilots who stayed in lunar orbit during a Moon landing: Mike Collins, Dick Gordon, Stu Roosa, Al Worden, Ken Mattingly, and Ron Evans.

Each of these astronauts stayed alone in the command module while two other astronauts landed on the Moon. At the highest point in their orbit, they were about 3,585 kilometers from their fellow astronauts.

From another point of view, this was the farthest the rest of humanity has ever managed to get from those jerk astronauts.

You'd think astronauts would have a lock on this category, but it's not so cut-and-dry. There are a few other candidates who come pretty close!

Polynesians

It's hard to get 3,585 kilometers^{[Because of the curve of the Earth, you actually have to go 3,619 kilometers across the surface to qualify.]} from a permanently inhabited place. The Polynesians, who were the first humans to spread across the Pacific, might have managed it, but this would have required a lone sailor to travel awfully far ahead of everyone else. It may have happened—perhaps by accident, when someone was carried far from their group by a storm—but we're unlikely to ever know for sure.

Once the Pacific was colonized, it got a lot harder to find regions of the Earth's surface where someone could achieve 3,585 kilometer isolation. Now that the Antarctic continent has a permanent population of researchers, it's almost certainly impossible.

Antarctic explorers

During the period of Antarctic exploration, a few people have come close to beating the astronauts, and it's possible one of them actually holds the record. One person who came very close was Robert Scott.

Robert Falcon Scott was a British explorer who met a tragic end. Scott's expedition reached the South Pole in 1911, only to discover that Norwegian explorer Roald Amundsen had beaten him there by several months. The dejected Scott and his companions began their trek back to the coast, but they all died while crossing the Ross Ice Shelf.

The last surviving expedition member would have been, briefly, one of the most isolated people on Earth.^{[Amundsen's expedition had left the continent by then.]} However, he (whoever he was) was still within 3,585 kilometers of a number of humans, including some other Antarctic explorer outposts as well as the Māori on Rakiura (Stewart Island) in New Zealand.

There are plenty of other candidates. Pierre François Péron, a French sailor, says he was marooned on Île Amsterdam in the southern Indian Ocean. If so, he came close to beating the astronauts, but he wasn't quite far enough from Mauritius, southwestern Australia, or the edge of Madagascar to qualify.

We'll probably never know for sure. It's possible that some shipwrecked 18th-century sailor drifting in a lifeboat in the Southern Ocean holds the title of most isolated human. However, until some clear piece of historic evidence pops up, I think the six Apollo astronauts have a pretty good claim.

Which brings us to the second part of Bryan's question: Were they lonely?

Loneliness

After returning to Earth, Apollo 11 command module pilot Mike Collins said he did not feel at all lonely. He wrote about the experience in his book Carrying the Fire: An Astronaut's Journeys:

Far from feeling lonely or abandoned, I feel very much a part of what is taking place on the lunar surface ... I don't mean to deny a feeling of solitude. It is there, reinforced by the fact that radio contact with the Earth abruptly cuts off at the instant I disappear behind the moon.

I am alone now, truly alone, and absolutely isolated from any known life. I am it. If a count were taken, the score would be three billion plus two over on the other side of the moon, and one plus God knows what on this side.

Al Worden, the Apollo 15 command module pilot, even enjoyed the experience:^{[BBC Future interview with Al Wolden (April 2, 2013)]}

There's a thing about being alone and there's a thing about being lonely, and they're two different things. I was alone but I was not lonely. My background was as a fighter pilot in the air force, then as a test pilot–and that was mostly in fighter airplanes–so I was very used to being by myself. I thoroughly enjoyed it. I didn't have to talk to Dave and Jim any more ... On the backside of the Moon, I didn't even have to talk to Houston and that was the best part of the flight.

Introverts understand; the loneliest human in history was just happy to have a few minutes of peace and quiet.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Lethal Neutrinos

How close would you have to be to a supernova to get a lethal dose of neutrino radiation?

(Overheard in a physics department)

The phrase "lethal dose of neutrino radiation" is a weird one. I had to turn it over in my head a few times after I heard it.

If you're not a physics person, it might not sound odd to you, so here's a little context for why it's such a surprising idea:

Neutrinos are ghostly particles that barely interact with the world at all. Look at your hand—there are about a trillion neutrinos from the Sun passing through it every second.

Ok, you can stop looking at your hand now.

The reason you don't notice the neutrino flood is that neutrinos hardly interact with ordinary matter at all. On average, out of that massive flood, only one neutrino will "hit" an atom in your body every few years.^{[Less often if you're a child, since you have fewer atoms to be hit. Statistically, my first neutrino interaction probably happened somewhere around age 10.]}

In fact, neutrinos are so shadowy that the entire Earth is transparent to them; nearly all of the Sun's neutrino flood goes straight through it unaffected. To detect neutrinos, people build giant tanks filled with hundreds of tons of material in the hopes that they'll register the impact of a single solar neutrino.

This means that when a particle accelerator (which produces neutrinos) wants to send a neutrino beam to a detector somewhere else in the world, all it has to do is point the beam at the detector—even if it's on the other side of the Earth!

Hey, these ones arrived faster than light! Wait, no.

That's why the phrase "lethal dose of neutrino radiation" sounds weird—it mixes scales in an incongruous way. It's like the idiom "knock me over with a feather" or the phrase "football stadium filled to the brim with ants".^{[Which would still be less than 1% of the ants in the world.]} If you have a math background, it's sort of like seeing the expression "ln(x)^e"—it's not that, taken literally, it doesn't make sense, but it's hard to imagine a situation where it would apply.^{[If you want to be mean to first-year calculus students, you can ask them to take the derivative of ln(x)e dx. It looks like it should be "1" or something, but it's not.]}

Similarly, it's so hard to get enough neutrinos to compel even a single one of them to interact with matter, making it hard to picture a scenario in which there'd be enough of them to affect you.

Supernovae^{["Supernovas" is also fine. "Supernovii" is discouraged.]} provide that scenario. The physicist who mentioned this problem to me told me his rule of thumb for estimating supernova-related numbers: However big you think supernovae are, they're bigger than that.

Here's a question to give you a sense of scale:

Which of the following would be brighter, in terms of the amount of energy delivered to your retina:

1. A supernova, seen from as far away as the Sun is from the Earth, or

2. The detonation of a hydrogen bomb pressed against your eyeball?

Can you hurry up and set it off? This is heavy.

Applying the physicist rule of thumb suggests that the supernova is brighter. And indeed, it is ... by nine orders of magnitude.

That's why this is a neat question; supernovae are unimaginably huge and neutrinos are unimaginably insubstantial. At what point do these two unimaginable things cancel out to produce an effect on a human scale?

A paper by radiation expert Andrew Karam provides an answer.^{[Karam, P. Andrew. "Gamma And Neutrino Radiation Dose From Gamma Ray Bursts And Nearby Supernovae." Health Physics 82, no. 4 (2002): 491-499.]} It explains that during certain supernovae, the collapse of a stellar core into a neutron star, 10⁵⁷ neutrinos can be released (one for every proton in the star that collapses to become a neutron).

Karam calculates that the neutrino radiation dose at a distance of one parsec^{[3.262 light-years, or a little less than the distance from here to Alpha Centauri.]} would be around half a nanosievert, or 1/500th the dose from eating a banana.^{[xkcd.com/radiation]}

A fatal radiation dose is about 4 sieverts. Using the inverse-square law, we can calculate the radiation dose: 2.3 AU is a little more than the distance between the Sun and Mars.

Core collapse supernovae happen to giant stars, so if you observed a supernova from that distance, you'd probably be inside the outer layers of the star that created it.

GRB 080319B was the most violent event ever observed—especially for the people who were floating right next to it with surfboards.

The idea of neutrino radiation damage reinforces just how big supernovae are. If you observed a supernova from 1 AU away—and you somehow avoided being being incinerated, vaporized, and converted to some type of exotic plasma—even the flood of ghostly neutrinos would be dense enough to kill you.

If it's going fast enough, a feather can absolutely knock you over.

Dude, AGAIN? Can you just pitch like a normal person?

i like you

Soda Planet

How much of the Earth's currently-existing water has ever been turned into a soft drink at some point in its history?

Brian Roelofs

0.0000005%.

First, a tiny bit of background: In the beverage industry, "soft drink" technically refers to any non-alcoholic packaged beverage, but it's commonly used to mean carbonated beverages.^{[In the US, the word people use to refer to a generic carbonated beverage—"soda" vs. "pop" vs. "coke"—strongly depends on where they live.]} Carbonated water was first produced in the 1700s, and gained popularity as "tonic water" (carbonated water mixed with quinine powder, which has anti-malaria properties), and in carbonated lemonade.^{[Shahan Cheong, Taking the Waters: The History of the Modern Soft-Drink, Not Yet Published (blog post)]}

The vast majority of all soft drinks ever consumed have been consumed in the last 40 years. Carbonated beverages were fairly popular in the industrialized world throughout the 20th century, but population growth and the spread of companies like Coca-Cola into the developing world mean that the total soda consumption per year has grown relatively fast.

Total soft drink consumption in 2013 was about 188 billion liters. That's 26 liters per person annually, or 70 mL/day.^{[MarketLine, Carbonated Soft Drinks: Global Industry Guide]} (In the US, the average was 170 liters, or about one 16-oz drink per person per day^{[Dan Check, Matt Dodson, and Chris Kirk, Americans Drink More Soda Than Anyone Else (slate.com)]}).

And each soda is a couple of Cadbury eggs.

Over the past several centuries, humans have probably consumed about 6.5 trillion liters of carbonated beverages.^{[This is a ballpark guess based on population growth and some rough estimates of when soda-drinking became popular in different parts of the world.]}

That's a lot, certainly. For example, it's enough to fill every house and apartment in the US to a depth of 12 inches:

BRB, searching Amazon for 'floor-length straw'.

Even if we assume that every soda is made from an entirely new batch of water, and doesn't include any water from previous sodas, it still represents a tiny fraction of the world's fresh water, and an even tinier fraction of the total volume of the oceans.

What if we expand the question to cover all drinking water? What percentage of water molecules have been drunk^{[Drank? Drinked? Drankéd?]} by someone at some point?

Humans have been around for a few hundred thousand years, and the total number of humans who have ever lived is usually estimated to be around 110 billion. The question of how much water we should drink per day is the subject of furious debate—the "8 glasses" thing seems to be a myth—but the amount of water we actually drink per day seems to be about a liter.^{[EPA, Estimated Per Capita Water Ingestion and Body Weight in the United States–An Update (2004)]} This amount varies a little depending on climate, but if we assume the average historical human drank a liter of water per day for 40 years,^{[This is a rough ballpark estimate; it's lower than the 70 or 80 years you might expect because we have to account for the changing human lifespans throughout history and the decreased water consumption by children.]} then our species has drunk about 100 trillion liters of water in total.

100 trillion liters (100 km³) is still very little compared to even the volume of all rivers (1,200 km³). This means that, since our drinking water passes through the water cycle and is quickly diluted by rivers and oceans, the majority of the water molecules we drink have never been drunk by any other human.^{[On the other hand, it's just about guaranteed that some of the water molecules in any mouthful have been drunk by someone else.]}

But we're just one species.

Dinosaurs, as a taxonomic group, have been around^{[They're still around!]} for 230 million years, but their heyday was the mid-to-late Jurassic period. In this period, there were probably around 5 trillion kilograms of dinosaur alive at any given time.^{[Jerzy Trammer, "Differences in global biomass and energy use between dinosaurs and mammals", Acta Geologica Polonica, Vol. 61 (2011), No. 2, pp. 125–132]} (Today, there are probably only a few hundred billion kilograms of living dinosaur,^{[I haven't been able to find an estimate for total global bird biomass, but I'll take any chance to cite my favorite journal article ever: "How Many Birds Are There?", by Kevin J. Gaston and Tim M. Blackburn, which estimates the total number at about 300 billion. A later paper lowered the estimate to about 80 billion, so unless the average bird weighs 140 lbs, there is far less dinosaur in the world today than in the Jurassic.]} 50 billion of it chicken).

If we assume Jurassic dinosaur water requirements were similar to mammal ones,^{[Animal weights and their food and water requirements]} then this suggests dinosaurs drank something like 10²² or 10²³ liters of water during the Mesozoic era—more than the total volume of the oceans (10²¹ liters).

The average "residence time" of water in the oceans—the amount of time a water molecule spends there before moving into another part of the water cycle—is about 3,000 years,^{[K. L. Schulz, Water in the Biosphere]} and no part of the water cycle traps water for more than a few hundred thousand years. This means we can assume that, over timescales of millions of years, Earth's water is thoroughly mixed—and dinosaurs had plenty of time to drink it all many times over.

This means that while the chances are that most of the water in your soda has never been in another soda, almost all of it has been drunk by at least one dinosaur.

::sluuuuuurp:: RRRRRR 'Sorry.'

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Phone Keypad

I use one of those old phones where you type with numbers—for example, to type "Y", you press 9 three times. Some words have consecutive letters on the same number. When they do, you have to pause between letters, making those words annoying to type. What English word has the most consecutive letters on the same key?

Stewart Bishop

We can answer that question with the following headache-inducing shell command, which finds all words in a given list which use the same key a bunch of times in a row:

cat wordlist.txt | perl -pe 's/^(.*)\$/\L\$& \U\$&/g' | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' '2223334445556667777888999' | grep -P "(.)\1\1\1\1\1"

The winner, according to this script, is nonmonogamous, which requires you to type seven consecutive letters (nonmono) with the "6" key.^{[It's actually tied with nonmonotonic. These no doubt both lose to more obscure words which weren't in the wordlists I used.]}

Phone Keyboard Sentences

It's rare for a word to have all its letters on the same key; the longest common ones are only a few letters.^{[Like "tutu".]} Nevertheless, using only these words, we can write a high def MMO on TV, a phrase whose words use only one number key each.

Just one more hour.

There are plenty of other phrases like this, although some of them are a bit of a stretch:

Pony up!

Typing issues like this aren't limited to old phone keyboards. For any text input system, you can find phrases which are weird to type.

QWERTY Keyboards

It's a well-known piece of trivia among word geeks that "stewardesses" is the longest common word you can type on a QWERTY keyboard using only the left hand.

In fact, it's possible to write entire sentences with just the left hand. For example, try typing the words We reserved seats at a secret Starcraft fest. Weird, huh?

Let's take a look at a few more sentences—written with the help of some even messier shell commands and Python scripts^{[I constructed these sentences by searching text logs for sentence fragments that fit a particular constraint, then randomly connecting those groups together using a technique called Markov chaining. You can see the code I used here.]}—which follow various constraints:

Left hand only

Totally worth it.

MEET SINGLE FERRETS IN YOUR AREA TONIGHT

Right hand only

How DARE you.

OMG puppy milk!

Home row only

He looked at the contents and immediately fell dead.

She's nice, though!

Crisp, though.

Top row only

Also, we brought some milk!

The worst part is it actually IS really good.

And lastly, if anyone wants to know why you're not more active on social media, you only need the top row to explain that you're ...

Or too pretty to retweet.

we turned to sleep deprived zombies in the streets of frankfurt and kissed for the new year, we had a year ahead just for the two of us, we had a life together

Reading Every Book

At what point in human history were there too many (English) books to be able to read them all in one lifetime?

Gregory Willmot

This is a complicated question. Getting accurate counts of the number of extant books at different times in history is very hard bordering on impossible. For example, when the Library of Alexandria burned, a lot of writing was lost,^{[On the other hand, a lot of Egyptian readers were probably excited to get out of overdue book fines.]} but how much writing was lost is hard to pin down. Some estimates range from 40,000 books to 532,800 scrolls,^{[The Great Library of Alexandria]} and other writers say that all those numbers are implausible.

Researchers Eltjo Buringh and Jan Luiten van Zanden used historical book catalogs to put together statistics on the number of books (or manuscripts) published annually per region.^{[Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries ]} By their figures, the rate of publication in the British Isles probably passed one manuscript per day in around the year 1075 CE.

Most of the manuscripts published in 1075 weren't in English, or even the variants of English common at the time. In 1075, literature was typically written in some form of Latin or French, even in areas where Old English was commonly spoken on the street.

The Canterbury Tales (written in the late 1300s) were part of a move toward vernacular English as a literary language, although they're not exactly readable to a modern eye:

Wepyng and waylyng, care and oother sorwe
I knowe ynogh, on even and a-morwe,'
Quod the Marchant, 'and so doon oother mo
That wedded been.

If my 9th grade English teacher is reading, ignore this, I TOTALLY understand that verse.

Even if we know how many manuscripts were published per year, in order to answer Gregory's question, we still need to know how long it takes to read a manuscript.

Rather than trying to figure out how long all the lost books and codices are, we can step back and take a longer view of things.

Writing speed

Tolkien wrote Lord of the Rings in 11 years, which means that he wrote at an average pace of 125 words per day, or less than 0.085 word per minute. Harper Lee wrote the 100,000-word To Kill a Mockingbird in two and a half years, for an average of 100 words per day, or 0.075 words per minute. Since To Kill a Mockingbird is her only published book, her lifetime average is 0.002 words per minute, or about three words per day.

Some writers are substantially faster. In the preface to Opus 200, the prolific writer Isaac Asimov estimated that he had published about 15,000,000 words between age 30 and 50. His average over his writing career might have been around 1 word per minute, and at times he was averaging writing several thousand words per day. (Over his entire life, his average dips as low as 0.5 words per minute.) Some pulp writers have even higher averages.

It's reasonable to assume historical writers had a similar range of speeds. You might point out that typing on a keyboard is more than twice as fast as writing a manuscript in longhand. But typing speed isn't a writer's bottleneck. After all, at a typing speed of 70 words per minute, it should only take 24 hours to type out To Kill a Mockingbird.

Well, they say to write what you know.

Typing and writing speeds are so different because the limit on writing speed is how quickly our brains can organize, produce, and edit stories. This "storytelling speed" has probably changed much less over time than our physical writing speed has.

This gives us a much better way to estimate when the number of books became too large to read.

The average person can read at 200-300 words per minute. If the average living writer, over their entire lifetime, falls somewhere between Isaac Asimov and Harper Lee, they might produce 0.05 words per minute over their entire lifetime.

If you were to read for 16 hours a day at 300 words per minute,^{[For an average of 200 words per minute.]} you could keep up with a world containing an average population of 100,000 living Harper Lees or 400 living Isaac Asimovs.

Isaacs Asimov?

If we estimate that during their active periods, writers are producing somewhere between 0.1 and 1 word per minute, then one dedicated reader might be able to keep up with a population of about 500 or 1,000 active writers. The answer to Gregory's question—the date at which there were too many English books to read in a lifetime—happened sometime before the population of active English writers reached a few hundred. At that point, catching up became impossible.

The magazine Seed estimates that the total number of authors reached this point around the year 1500 and has continued rising rapidly ever since.^{[Seed: A Writing Revolution]} The number of active English writers crossed this threshold shortly thereafter, around the time of Shakespeare, and the total number of books in English probably passed the lifetime reading limit sometime in the late 1500s.

On the other hand, how many of them would you want to read? If you go to goodreads.com/book/random, you can see a semi-random sample of what you'd be reading. Here's what came up for me:

• • School Decentralization in the Context of Globalizing Governance: International Comparison of Grassroots Responses, by Holger Daun
• • Powołanie (Dragon Age #2), by David Gaider
• • An Introduction to Vegetation Analysis: Principles, Practice and Interpretation, by David R. Causton
• • AACN Essentials of Critical-Care Nursing Pocket Handbook, by Marianne Chulay
• • National righteousness and national sin: the substance of a discourse delivered in the Presbyterian church of South Salem, Westchester co., N.Y., November 20, 1856, by Aaron Ladner Lindsley
• • Phantom of the Auditorium (Goosebumps #24), by R. L. Stine
• • High Court #153; Case Summaries on Debtors and Creditors-Keyed to Warren, by Dana L. Blatt
• • Suddenly No More Time, by Emil Gaverluk

So far, I've read ... the Goosebumps book.

To make it through the rest, I might need to recruit some help.

'Can't I skip my OWN books? There are so many of them!' 'No, Isaac. You know the rules.'

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Growth Rate

What height would humans reach if we kept growing through our whole development period (i.e. till late teens/early twenties) at the same pace as we do during our first month?

Maria

Tall.

According to the National Center for Health Statistics, the average newborn's height (length) is approximately 0.5 meters,^{[or 0.56 meters in heels.]} or a quarter of the diameter of the Death Star thermal exhaust port.

Babies are a little less than a quarter of a womp rat long.

From this initial height of 0.5 meters, they grow to about 1.5 or 2.0 meters:

The timing of male and female puberty roughly cancel out, so average height grows steadily throughout the Kidz Bop years.

Babies grow fastest right after they're born. During their first month, infants grow about 4.4 centimeters, ten times their growth rate during their early teenage years.

A chart showing a lower bound for the length of a baby-eating snake versus age of its victims.

In Maria's scenario, this growth rate continues until about age 20:

We're going to need a longer snake.

Let's follow that child's growth over the years.

By its first birthday, the baby would be a meter long:

Go get another one-gallon bottle.

At 2 years and 3 months, the kid would reach 169 centimeters (5'7"), the average adult height in the US.

Blends right in!

By age 3, we'd have a 2.08 meter (6'10") toddler, taller than Darth Vader ...

I find the bug you found disturbing.

... and much taller than Yoda:

MMmmmm. An excellent bug this is!

By age 4, the child would be nearly nine feet tall, able to dunk a basketball without jumping.^{[A 7'8" Harlem Globetrotters player can almost dunk without jumping, so the threshold for a clear no-jump dunk is probably around 8 feet.]}

But what I really want to do is play professional baseball.

A few months later, the kid would surpass Robert Wadlow to become the tallest human in history.

At age 5, the child would be $ \pi $ meters tall (10'4"):

I mean, 0.5 tau meters.

At age 7, the child would be 4.2 meters tall, able to stare down a T-rex:

*purrrrr*

By age 10, the child would be 5.8 meters tall (19 feet). If we assume these giants are proportioned like adult humans, this kid would weigh over a metric ton.

Still only about 0.2 tyrannosaurs.

Actual humans wouldn't be able to grow to such heights. Thanks to the square-cube law, our bones would be too thin to support our weight and our hearts would be unable to pump blood around our bodies. Even breathing would be difficult; we might be able to position ourselves to keep our airways opened, but to breathe in a lungful of air would require very high airflow rates; we'd experience tornado winds all the way down our airways.

Our giant would reach a final height of between 10 and 12 meters, assuming growth tapered off around age 20. At that height, they'd be able to comfortably dunk a basketball while keeping one hand on the court outside the three-point line.^{[A creative NBA 2K3 mod shows us what that player might look like.]}

What do you mean 'against the rules'? Your team has a freakin' golden retriever!

In addition to the insurmountable health problems, someone with this rapid growth rate would face another hardship.

To ride roller coasters, you have to be above a certain minimum height. However, they generally also have a maximum height.

You must have a core temperature between 33°C and 41°C to ride.

Bizarro, a coaster at Six Flags New England, has a minimum height of 137 cm (4'6") and a maximum height of 193 cm (6'4"). Our child would be tall enough to ride Bizarro at age 2 ... and too tall by age 3. Their coaster-riding window would last only 387 days.

It's a sad truth: Roller coasters just aren't for everyone.

That night, the roller coaster's empty cars are all mysteriously lifted from their tracks and smashed to the ground.

and we flew, for each of us, it was the first time we were flying with someone and i couldn't have been happier to be with you

T-rex Calories

If a T-rex were released in New York City, how many humans/day would it need to consume to get its needed calorie intake?

Tony Schmitz

About half of an adult, or one ten-year old child:

Shoot, I forgot to eat one yesterday. Am I allowed to double up?

Tyrannosaurus rex weighed about as much as an elephant.^{[This always seemed a little off to me; my mental image of elephants is that they're in the same size range as cars or trucks, whereas T-rex, as Jurassic Park showed, is big enough to stomp on cars. But a Google image search for car+elephant shows elephants looming over cars just like the T-rex in Jurassic Park. So, great, now I'm also afraid of elephants.]}

Utahraptor will be so jealous.

No one is totally sure what dinosaur metabolism looked like, but the best guesses for how much food T-rex ate seem to cluster around 40,000 calories per day.^{[Food calories (kcal). Sources: This and this, and this with some notes from this and distraction from this. ]}

If we assume dinosaurs had metabolisms similar to today's mammals, they'd eat a lot more than 40,000 calories each day. But the current thinking is that while dinosaurs were more active (loosely speaking, "warm-blooded") than modern snakes and lizards, very large dinosaurs probably had metabolisms that more closely resembled komodo dragons than elephants and tigers.^{[For big sauropods, we know this must be the case, because otherwise they would overheat. However, there's a lot of uncertainty surrounding T-rex-sized dinosaurs.]}

Next, we need to know how many calories are in a human. This number is helpfully provided, by Dinosaur Comics author Ryan North, on this wonderful t-shirt. Ryan's shirt tells us that an 80-kg human contains about 110,000 calories of energy.

Therefore, a T-rex would need to consume a human every two days or so.^{[Although a T-rex would likely be willing to eat several days to weeks worth of food in one meal, so if it has the option, it might eat a bunch of people at a time, then go for a while without eating.]} The city of New York had 239,736 births in 2011, which could support a population of about 1,000 tyrannosaurs. However, this ignores immigration—and, more importantly, emigration, which would probably increase substantially in this scenario.

I wonder if a tyrannosaur could fit into an MTA subway car.

The 33,000 McDonald's restaurants worldwide sell something like 15 billion hamburger patties per year,^{[They stopped reporting the "x billions served" number on their signs, but this website has some extrapolations.]} for an average of 1,245 burgers per restaurant per day. 1,245 burgers is about 600,000 calories, which means that each T-rex only needs about 80 hamburgers per day to survive, and one McDonald's could support over a dozen tyrannosaurs on hamburgers alone.

One of them sleeps in the ball pit. Tell your kids!

Ands if you live in New York, and you see a T-rex, don't worry. You don't have to choose a friend to sacrifice; just order 80 burgers instead.

And then if the T-rex goes for your friend anyway, hey, you have 80 burgers.

More of an acquaintance, really.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Lake Tea

What if we were to dump all the tea in the world into the Great Lakes? How strong, compared to a regular cup of tea, would the lake tea be?

Alex Burman

Weak, bordering on homeopathic.

The standard cup of tea, as described by the International Organization for Standardization in ISO 3103, contains two grams of tea per 100 mL of water.^{[Further ISO standards concerning tea include ISO 3720 (black tea), ISO 11287 (green tea), and ISO 14502-2 (the difference between black tea and green tea).]} The Great Lakes have a volume of about 22,600 cubic kilometers, which means we would need about 450 billion tons of tea to reach proper strength.

According to the Tea Board of India, one year's global tea harvest totals only about 4.8 million tons,^{[Using figures from this report extrapolated forward to 2014.]} only 1/100,000th of what we'd require to make Great Lake Tea. If we dumped those 4.8 million tons into the lakes, the resulting tea would be about as strong as if we'd dripped two drops of tea in a bathtub.^{[Technically, calling this kind of tea "homeopathic" is an exaggeration, since substances in homeopathy are diluted way more than this.]} Proper bathtub tea, of course, requires one 3-kg bag.

Cue strong opinions about adding sugar to bathtubs.

For better lake tea, we should find a lake with a volume of 240 million cubic meters (0.24 cubic kilometers).

Wular Lake in Kashmir is one candidate. Its volume varies with the seasons, but during the winter it's just about exactly the right size.^{[Unfortunately, it's shrinking. (For winter volume, see the chart on page 18 of that report.)]} India is the world's second-largest tea producer, so it's also conveniently located.

Ullswater, in the UK's Lake District, is another great candidate. With a relatively stable year-round volume of about 0.23 cubic kilometers, it would be an excellent site for brewing a global cup of tea.

Of course, while neither Wular Lake or Ullswater has ever been used as a giant teakettle, something like this was—famously—attempted in my own backyard in Boston. In 1773, a group of colonists disguised as American Indians<sup>[They dressed up as American Indians to align themselves politically with the Americas—against Britain—invoking the popular European stereotype of the free and noble savage.

The Mohawk people, the actual Indians who the protesters were mimicking, mistrusted the settlers encroaching on their land, sided with the British during the subsequent war, and afterward were driven from their homes by the Americans and fled to Canada.]</sup> boarded three British ships and threw the cargo of tea—around 44 tons of it—into Boston Harbor to protest British-run tax policy.

Boston Harbor has a volume of about 0.44 cubic kilometers, which means that the "tea" brewed in 1773 would have been even more dilute than our Great Lakes tea. The harbor is also somewhat larger^{[The tidal range in Boston is so large (over three meters) that the harbor's volume at high tide is nearly double what it is at low.]} than Wular Lake or Ullswater, so all the tea in the world would still make Boston Harbor slightly too weak.

Although it's a lot better since we built that treatment plant and stopped dumping all our raw sewage in.

There's another problem: Heat. If you wanted to make tea from a lake, such as Ullswater or Wular Lake, you'd have to heat the water up. Is that even possible?

There's clearly enough stored energy in the world to do it. After all, we presumably heat that amount of water for tea every year already; we just do it in small batches around the world.

To heat up Ullswater to 80°C^{[Lots of people have very strong opinions on what this temperature should be. Please direct any corrections on this matter to What-If Tea-Related Complaints Dep't, c/o Her Majesty The Queen, Buckingham Palace, London SW1A 1AA.]} would take joules of energy—about 20 days worth of British electricity consumption. which is roughly what would be released if you dropped a water bottle full of antimatter in the lake.

Not a significant source of riboflavin.

Asking Britain to go without electricity for 20 days just to fill one of their lakes with tea seems like it might be a hard sell. Fortunately, there's an easier solution.

Boiling Lake in Dominica is a volcanic lake about 60 meters across. Its temperature varies, but it's often near boiling at the edges and vigorously boiling in the center. Measuring the depth of the lake is difficult, so it's hard to get an estimate of the total volume.

The fact that it seems to boil away sometimes doesn't help.

Frying Pan Lake in New Zealand, on the other hand, is the largest hot lake in the world. It has a volume of about 200,000 m³, and an average temperature of around 50°C—not quite hot enough for tea, but much closer than Ullswater or Wular Lake.

New Zealanders consume about 600 grams of tea per person,^{[Kerryn Pollock. 'Tea, coffee and soft drinks', Te Ara - the Encyclopedia of New Zealand, updated 15-Jul-13]} for a total of 2,700 tons of tea. If they waited until Frying Pan Lake got particularly hot, then dunked it all in at once ...

We are making a good decision by doing this thing we read on a blog. We are going to have so much tea.

... they could brew a year's worth of tea in minutes.

we went on trying foods and making plans

Pile of Viruses

What if every virus in the world were collected into one area? How much volume would they take up and what would they look like?

Dave

It would be a huge pile, but human viruses would make up only a tiny fraction of it.

HIV, the virus that causes AIDS, has killed tens of millions of people worldwide, and over 30 million people are currently living with HIV. The number of copies of the virus carried in someone's blood can vary dramatically,^{[Data on viral load—the number of copies of the virus per mL of blood—can be found in this paper.]} but across all the people in the world, there probably exists about a spoonful worth of HIV.

You should wash that spoon before you use it again.

The typical healthy human body contains about viruses. This is actually not as many as you might expect; by volume, humans are apparently a less friendly environment for viruses than, say, soil.^{[An area of wetlands in Delaware contains something like four billion viruses per mL of soil, in case you were looking for a fun vacation destination.]}

If you gathered together all the viruses in all the humans in the world, they would fill about ten oil drums:

So the world currently has about a 200,000,000,000:1 oil reserve:human virus ratio. I'm sure this number has some economic significance.

These 10 barrels only represent a tiny portion of the global virus community. Most of the world's viruses aren't found in humans. They're found in the sea.

Seawater is full of microorganisms, and we've recently learned that those microorganisms are preyed on by viruses in a big way. Every day, about one in five living cells in the ocean is killed by a virus.^{[Marine viruses—major players in the global ecosystem]} These viruses are found from the surface of the ocean down to the depths.^{[Oddly, as you go further offshore and further down, the concentration of viruses doesn't decrease as much as the concentration of bacteria, so the virus-to-bacteria ratio is higher in the deep oceans than near the shore. ]} Because the sea is so big,^{[Citation: Go and look at the sea. It's big.]} it contains a staggering number of viruses.

If you piled up all these viruses—more than 10³⁰ of them—in one place, they would be the size of a small mountain.

It would be a little smaller than Mount Royal in Montreal.

It's hard to say exactly what the virus mountain would look like, but it would probably resemble something in between pus and meat slurry.^{[Blame Dave—he's the one who asked.]} Regardless of its exact appearance, it would almost certainly be disgusting.

The CDC recommends that to avoid infection, you should pour globs of pure virus into the crook of your arm instead of directly onto your hand.

The pile wouldn't stay mountain-shaped for long, any more than a mountain of any organic secretion would.^{[If you don't believe me, try building a mountain of earwax or snot. You'll find you can't make it higher than a few inches before your friends and family show up and sit you down for a talk.]} To avoid a gigantic flood, it might be better to collect them into some kind of container.

MetLife Stadium, host of Super Bowl XLVIII, has a volume of about 1.5 million cubic meters. Earth's viruses could fill the stadium about 150 times over.

So if you watch the Super Bowl, take a moment to picture all the players floating, suspended, in a sea of yellowish-white secretions.

Belichick has his revenge.

Enjoy the game!

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Catch!

Is there any way to fire a gun so that the bullet flies through the air and can then be safely caught by hand? e.g. shooter is at sea level and catcher is up a mountain at the extreme range of the gun.

Ed Hui, London

Yes.

The "bullet catch" is a common magic trick in which a magician appears to catch a fired bullet in mid-flight—often between their teeth. This an illusion, of course; it's not possible to catch a bullet like that.^{[This was confirmed by Mythbusters in episode 4 of Season 4.]}

But under the right conditions, you could catch a bullet. It would just take a lot of patience.^{[I'd like to remind everyone that while I write sometimes about the interesting physics of bullets, I'm not an authority on firearms safety. I was raised Quaker; I've never held a gun, much less fired one.]}

A bullet fired straight up would eventually reach a maximum height.^{[Don't do this. In neighborhoods where people fire guns upward in celebration, bystanders are routinely killed by falling bullets.]} It probably wouldn't stop completely; more likely, it would be drifting sideways at a couple meters per second. At that speed, as long as you were in the right place at the right time, you could snatch it out of the air.

If someone fired a bullet upward ...

Goodnight, Moon.

... and you were hanging out in a hot-air balloon directly above the firing range ...

Hmm. For every bullet I catch, I'll need to drop a tiny sandbag.

... it's possible that you could reach out and snag the bullet at the apex of its flight.

If you succeeded, you might notice something odd: In addition to being hot, the bullet would be spinning. It would have lost its upward momentum, but not its rotational momentum; it would still have the spin given to it by the barrel of the gun.

(We're in the northern hemisphere.)

This effect can be seen, dramatically, when a bullet is fired at ice.^{[Floor water.]} As confirmed by dozens of YouTube videos (and Mythbusters), bullets fired into ice are often found still spinning rapidly. You'd have to grab the bullet firmly; otherwise, it might jump out of your hand.

If you don't have a balloon, you could potentially make this work from a mountain peak. Mount Thor, which you may remember from question #51, features a vertical drop of 1,250 meters. According to ballistics lab Close Focus Research, this is almost exactly how high a .22 Long Rifle bullet will fly if fired directly upward.^{[Close Focus Research, Maximum Altitude For Bullets Fired Vertically]}

Oh, never mind, whoever was shooting just fell into the cotton candy pit.

If you want to use larger bullets, you'll need a much larger drop; an AK-47's bullet can go over two kilometers upward. There are no purely vertical cliffs that are that tall, so you'd need to fire the bullet at an angle, and it would have significant sideways speed at the top of its arc. However, a suitably tough baseball glove might be able to snag it.^{[In fact, according to Rifle Magazine, a gun writer once claimed that at a thousand yards, he could catch ordinary rifle bullets with a baseball glove. Of course, he was being figurative—you wouldn't see the bullet coming, so you'd be just as likely to catch it with your face as with your glove.]}

In any of these scenarios, you'd have to get extraordinarily lucky. Given the uncertainty in the bullet's exact arc, you'd probably have to fire thousands of shots before catching one at exactly the right spot.

And by that point, you may find you've attracted some attention.

He gave my scarecrow friend a prestigious degree that turned out to be TOTALLY USELESS for finding a job!

we wanted to see the world, israel, egypt, india, laos, malaysia, nepal, tunisia

Hitting a comet

Astrophysicists are always saying things like "This mission to this comet is equivalent to throwing a baseball from New York and hitting a particular window in San Francisco." Are they really equivalent?

Tom Foster

No; the baseball thing is much harder.

How are you even supposed to throw this thing?

To throw something from New York to LA, you have to lob it out of the atmosphere like an ICBM.^{[Launched by New York at LA, as I'm sure happens now and then.]}

Unfortunately, baseballs are too small to punch through the atmosphere. No matter how fast they're going, they'll wind up stopping before they make it to space. If you wanted to hit a window in LA with a baseball, you'd have better luck throwing it at a plane and hoping it gets lodged in the landing gear during takeoff.

The comet-visiting spacecraft Tom's astrophysicists are referring to is probably Rosetta, which is about to orbit the comet 67P/Churyumov–Gerasimenko and send a lander down to its surface.

Note: 67P/Churyumov–Gerasimenko is a mouthful, so for the rest of this article I'm just going to call the comet "Kevin".

Rosetta is currently about to arrive at Kevin, and is about 780 million kilometers from Earth. It's taken a roundabout route:

Rosetta got gravitational assists from several flybys of Earth and one of Mars, flew past two asteroids, and—in a maneuver that still has some at ESA confused—became the first spacecraft to do a flyby of itself.

Kevin, Rosetta's target, is about 4 km wide. Since it's 780 million kilometers away. If it were as far away as San Francisco is from New York, the target would be two centimeters wide—even more impressive than the statistic Tom quoted.

So Rosetta hitting its target is like throwing an object from New York and having it hit a particular key^{[Tilde, if you're curious.]} on a keyboard in San Francisco.

I TOLD you to aim for SAVE!

It's not a fair comparison, but you gotta admit, it sounds pretty precise. I once heard an account from someone who worked on the Cassini-Huygens mission, where one of the designers pointed out that their spacecraft traveled to a target a billion kilometers away, and arrived within something like a second and a half of the scheduled time.^{[Despite searching, I've been unable to track down this interview. If you see it, let me know!]}

On the other hand, we could make less flattering comparisons.

Take remote surgery. If a surgeon in New York uses a remote surgery robot in San Francisco to do eye surgery, and the robot aims for the patient's eye with the precision of Rosetta's approach, it will point its laser somewhere around here:

At least it'll help clear my sinuses.

However this isn't a fair comparison either. Both Rosetta and our laser surgeon^{[I really hope that's what this job is called]} will refine their movements as they make their final approaches, achieving very high precision.

When it comes down to it, the two tasks—remote surgery and remote probe-landing—are probably about equally precise, in a distance sense.

Which brings me to something a little different with which I'd like to end this article: A question for you to try to answer. Namely:

Would you rather bet a million dollars on a spacecraft landing engineer's ability to successfully perform eye surgery, or an eye surgeon's ability to land a probe on a comet?

I haven't been able to decide.

But don't worry; that's a rare complication, only happening in one in every 20 or 30 procedures.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Star Sand

If you made a beach using grains the proportionate size of the stars in the Milky Way, what would that beach look like?

Jeff Wartes

Sand is interesting.^{[Citation needed]}

"Are there more grains of sand than stars in the sky?" is a popular question which has been tackled by many people. The upshot is that there are probably more stars in the visible universe than grains of sand on all of Earth's beaches.

When people do those calculations, they often dig up some good data on the number of stars, then do some hand-waving about sand grain size to come up with a number for the sand grains on Earth.^{[From a practical point of view, geology and soil science are more complicated than astrophysics.]} We're not going to tackle that issue today, but to answer Jeff's question, we do need to figure out what the deal with sand is.<sup>["i like sand because i don't really know what it is and there's so many of it"

—@darth__mouth]</sup> Specifically, we need to have some idea of what grain sizes correspond to clay, silt, fine sand, coarse sand, and gravel, so we can understand how our galaxy would look and feel if it were a beach.^{[Instead of just containing a bunch of them.]}

Fortunately, there's a wonderful chart by the US Geologic Survey that answers all these questions and more. For some reason, I find this chart very satisfying—it's like the erosion geology edition of the electromagnetic spectrum chart.

According to surveys of sand,^{[There are apparently lots of them.]} the grains found on beaches tend to run from 0.2mm to 0.5mm (with the finest layers on top). This corresponds to medium-to-coarse sand in the chart. The individual grains are about this big:

(sandisk)

If we assume the Sun corresponds to a typical sand grain, then multiply by the number of stars in the galaxy, we come up with a large sandbox worth of sand.^{[I mean, you come up with a bunch of numbers, but imagination turns them into a sandbox.]}

However, this is wrong. The reason: Stars aren't all the same size.

There are a number of widely-circulated YouTube videos comparing star sizes. They do a good job of getting across just how staggeringly large some stars are. Although it's easy to get lost in the videos and lose track of scale, it's clear that some of the grains in our sandbox universe would be more like boulders.

Here's how the main-sequence^{[The stars in the main part of their fuel-burning lifecycle.]} star-sand grains look:

These stars are all technically called 'dwarf' stars. Astronomers could learn a thing or two about straightforward nomenclature from the sand-grain geologists.

They mostly fall into the "sand" category, though the larger Daft Punk stars cross the line into "granules" or "small pebbles".

However, that's just the main sequence stars. Dying stars get much, much bigger.

They're almost as big as SD cards!

When a star runs out of fuel, it expands into a red giant. Even ordinary stars can produce huge red giants, but when a star that's already massive enters this phase, it can become a true monster. These red supergiants are the largest stars in the universe.

I have a vague feeling that I shouldn't be looking directly at this rock.

These beachball-sized sand stars would be rare, but the grape-sized and baseball-sized red giants are relatively common. While they're not nearly as abundant as Sun-like stars or red dwarfs, their huge volume means that they'd constitute the bulk of our sand. We would have a large sandbox worth of grains ... along with a field of gravel that went on for miles.

This beach sucks.

The little sand patch would contain 99% of the pile's individual grains, but less than 1% of its total volume. Our Sun isn't a grain of sand on a soft galactic beach; instead, the Milky Way is a field of boulders with some sand in between.

But, as with the real Earth seashore, it's the rare little stretches of sand between the rocks where all the fun seems to happen.

Just to be clear, this image does not update every hour.

and we wanted to find a community in spain

Paint the Earth

Has humanity produced enough paint to cover the entire land area of the Earth?

—Josh (Bolton, MA)

This answer is pretty straightforward. We can look up the size of the world's paint industry, extrapolate backward to figure out the total amount of paint produced. We'd also need to make some assumptions about how we're painting the ground. Note: When we get to the Sahara desert, I recommend not using a brush.

I hear a film director actually did this once, in the days before digital color correction.

But first, let's think about different ways we might come up with a guess for what the answer will be. In this kind of thinking—often called Fermi estimation—all that matters is getting in the right ballpark; that is, the answer should have about the right number of digits. In Fermi estimation, you can round^{[Using the formula , meaning that 3 rounds to 1 and 4 rounds to 10.]} all your answers to the nearest order of magnitude:

Legs per cat: 10

Let's suppose that, on average, everyone in the world is responsible for the existence of two rooms, and they're both painted. My living room has about 50 square meters of paintable area, and two of those would be 100 square meters. 7.15 billion people times 100 square meters per person is a little under a trillion square meters—an area smaller than Egypt.

My vote for Lizard People was thrown out.

Let's make a wild guess that, on average, one person out of every thousand spends their working life painting things. If I assume it would take me three hours to paint the room I'm in,^{[This is probably optimistic, especially if there's an internet connection in the room.]} and 100 billion people have ever lived, and each of them spent 30 years painting things for 8 hours a day, we come up with 150 trillion square meters ... just about exactly the land area of the Earth.

It's a tie!

How much paint does it take to paint a house? I'm not enough of an adult to have any idea, so let's take another Fermi guess.

Based on my impressions from walking down the aisles, home improvement stores stock about as many light bulbs as cans of paint. A normal house might have about 20 light bulbs, so let's assume a house needs about 20 gallons of paint.^{[These are very rough estimates.]} Sure, that sounds about right.

The average US home costs about \$200,000. Assuming each gallon of paint covers about 300 square feet, that's a square meter of paint per \$300 of real estate. I vaguely remember that the world's real estate has a combined value of something like \$100 trillion,^{[Citation: This really boring dream I had once.]} which suggests there's about 300 billion square meters of paint on the world's real estate. That's about one New Mexico.

'Lizard People' demands a recount.

Of course, both of the building-related guesses could be overestimates (lots of buildings are not painted) or underestimates (lots of things that are not buildings^{[EXAMPLES OF THINGS THAT ARE NOT BUILDINGS: Ducks, M&Ms, cars, the Sun, cuttlefish, microchips, Macklemore, lightning, goat blood, zeppelins, tapeworms, pickle jars, those sticks you use to toast marshmallows, alligators, tuning forks, minotaurs, Perseid meteors, ballots, crude oil, sponsored tweets, and catapults that throw handfuls of engagement rings.]} are painted) But from these wild Fermi estimates, my guess would be that there probably isn't enough paint to cover all the land.

So, how did Fermi do?

According to the report The State of the Global Coatings Industry, the world produced 34 billion liters of paints and coatings in 2012.

There's a neat trick that can help us here. If some quantity—say, the world economy—has been growing for a while at an annual rate of n—say, 3% (0.03)—then the most recent year's share of the whole total so far is , and the whole total so far is the most recent year's amount times .

If we assume paint production has, in recent decades, followed the economy and grown at about 3% per year, that means the total amount of paint produced equals the current yearly production times 34.^[] That comes out to a little over a trillion liters of paint. At 30 square meters per gallon,^{["Square meters per gallon" is a pretty obnoxious unit, but I think it's not quite as bad as acre-foot (a foot by a chain by a furlong), which is an actual unit used in technical papers I was trying to read this week.]} that's enough to cover 9 trillion square meters—about the area of the United States.

So the answer is no; there's not enough paint to cover the Earth's land, and—at this rate—probably won't be enough until the year 2100.

Score one for Fermi estimation.

Two movies called Star Trek, one called Star Trek II, one called Star Trek III, and a BUNCH of movies called Star Trek X.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Rocket Golf

Assuming that you have a spaceship in orbit around the Earth, could you propel your ship to speeds exceeding escape velocity by hitting golf balls in the other direction? If so, how many golf balls would be required to reach the Moon?

—Dan (Kanata, Ontario)

It depends how good your swing is.

That sounds glib, but it's sort of true. The answer to this question hinges on exactly how fast you can hit a golf ball.

Sometimes, exact numbers don't matter that much. If my baseball, car, dog, or Zamboni goes a little faster than yours,^{[$20 says they will!]} it will go a little farther. But that's not how it works in rocket golf. The design of our spaceship turns out to involve an equation where the speed of the golf ball is in the exponent. That means a small change in speed can make a big difference.

The equation in question—which might be my favorite in all of physics—the Tsiolkovsky rocket equation:

This equation comes up a lot in What If calculations. I like it both because it says something fundamental about our ability to explore the universe, and because you can use it to get really good at Kerbal Space Program.

With some rearranging, the equation can help us figure out how much of our ship's weight has to be golf balls:

Someone who, like me, has never been golfing before, might—after swinging and missing a few times—manage to hit the ball at 120 mph (50 m/s).^{[See Trackman's page on ball speed]} To get to the Moon from low Earth orbit, you would need enough fuel to add 5,300 m/s to your ship's speed. By putting those numbers into the rocket equation, we can find out how large a sack of golf balls would have to be for the average golfer to reach the Moon. If we plug it in to Wolfram|Alpha ...

I didn't end up getting banned this time.

... we find that the bag of golf balls will have to be just about exactly 100 billion miles in diameter. That's much, much bigger than our Solar System.^{[As a Fermi rule of thumb, planets in the inner Solar System are 100 million kilometers away and planets in the outer Solar System are a billion kilometers away. Or miles; either one works.]}

Not pictured: Pretty much anything that isn't golf balls.

It would also promptly and violently collapse into a black hole.

Fortunately, we should be able to avert that disaster by making relatively small changes to the "120" in that equation. If we increase the golf ball's speed from 120 mph to 150, it shrinks the answer dramatically, and the required number of golf balls would fit snugly between the Sun and Mars. Still too big to avoid a catastrophic collapse, but we're getting somewhere.

Not pictured: Earth, which is in the bag of golf balls.

Tiger Woods can hit a golf ball at about 180 mph, which means that if he were powering our spaceship, the bag of golf balls would be only twice the diameter of the Sun!

I think it's tennis balls.

According to the Guinness Book of World Records, the record for fastest golf drive is 211 mph, set by Maurice Allen in 2012. This corresponds to a bag of golf balls only 100,000 kilometers across—smaller than Jupiter, but still (obviously) not practical.

However, golfer Ryan Winther claims to have beaten this record, though without Guinness observers there.^{[And, obviously, it doesn't count unless it's overseen by people from a beer company. If you want to set a world record, hit a golf ball at a radar gun and get it certified by the Mike's Hard Lemonade people.]} His ball speed was measured by something called the "Titleist Performance Institute" to be 226.7 mph, and he claims a personal best of 237 mph. If he could consistently hit 237 mph, we could shrink our fuel container down to the size of Earth^{[Although it would still be large enough to partially collapse under its own gravity, similar to what happened to the mole of moles.]}

Golf courses occupy about 1/20,000th of the world's total land area. On a desk globe, they would be about this big: o

This still wouldn't work; even in a high orbit, the massive tides from your ship—which is much more massive than the Moon—would be highly disruptive.

We could probably shrink the fuel tank further by using "illegal" equipment. There are Superball-style balls and "trampoline face" clubs which can hit much farther, and which would not be permitted in tournament play.^{[On the other hand, we're talking about a sport that brought whites-only clubs with it into the 21st century, and Agusta, host of the Masters, admitted its first woman in 2012. So maybe we shouldn't worry too much about their traditional rules.]} A hypothetical 270 mph drive would allow a fuel tank the size of the Moon.

At this point, why are we even using a club?

According to research from the US Air Force Academy and BTG Research,^{[Oddly, both researchers have the name "Courtney". There are probably about 200,000 people in the US named Courtney (first or last); maybe we should recruit them to all build potato cannons.]} a potato cannon fueled by acetylene can launch a potato at 140 m/s (310 mph). If it were capable of launching golf balls at that speed,^{[We're not factoring in the weight of the acetylene—but then again, we also weren't factoring in the weight of the hamburgers the golfer would need to eat to keep hitting those drives.]} our ship would have a diameter of only 150 miles!

LOOK OUT SPACE STATION AHEA-- ... uh, never mind. Oops.

There's the small problem that manufacturing that many golf balls would cost quintillions of dollars. You could bring the size down further by making the potato cannon more and more powerful and efficient, but at that point you're simply building a rocket.

And the potato cannon scenario has an extra perk. If you somehow made the balls durable enough to survive atmospheric entry, and you set up your maneuver so the ejected golf balls covered the middle latitudes evenly, then over the course of this maneuver you would be statistically likely to hit a hole-in-one ... at every golf course in the world.

The ones that landed in the water would have enough volume to raise the water level substantially—except on the Dead Sea, where they'd float on the surface.

we were torn between choices, and shredded by the shittiness of ecosea

Far-Traveling Objects

In terms of human-made objects, has Voyager 1 travelled the farthest distance? It's certainly the farthest from Earth we know about. But what about the edge of ultracentrifuges, or generator turbines that have been running for years, for example?

Matt Russell

Spacecraft go a lot faster than centrifuges.^{[With a few exceptions, as you'll see in the next footnote.]} Spacecraft travel at speeds measured in kilometers per second, and they maintain those speeds constantly. Machine parts rarely move faster than a few hundred meters per second, which means that they probably won't catch up.

But the precise answer to this question depends on what reference frame we're using. Let's go through a few of the options:

Measured relative to the Sun

As far as moving through the Solar System goes, Voyager 1 is one of the slowest manmade objects.^{[It's not the very slowest—that title might belong to the Galileo spacecraft. On September 6th, 1996 at 10:57 (UT), Galileo's speed relative to the Sun dropped to 276 meters per second (618 mph), making it possibly the slowest manmade object in Solar System history.]} It's moving at an average speed of about 16 km/s, which is barely half of the Earth's orbital speed around the Sun.

It might seem a little intuitively weird that Voyager 1, which went fast enough to escape the Solar System, is going slower than Earth, which didn't. But it makes more sense if you think of the Solar System as a furious whirlpool with the planets caught in it. Voyager 1 (partly by pushing off those planets) managed to go fast enough that it was flung from the whirlpool, and is now drifting sedately across the water's surface.^{[And will continue doing so forever, unless we go get it.]}

In other words, every 1977 Plymouth Voyager van has traveled farther than Voyager 1.

And more people have had sex in Plymouth Voyagers than Voyager spacecraft, unless NASA JPL is a wilder place than I thought.

The longest-traveled manmade objects, by this measure, aren't spacecraft at all—they're whatever objects have been on the Earth the longest, and have thus traveled the farthest around the sun. The first known surviving manmade objects are 2.6-million-year-old stone tools from Ethiopia, which have traveled a total of about 250 light-years.

By comparison, the most well-traveled space probe (possibly the defunct Mariner 10, which has been in a relatively tight loop around the Sun for decades) has only traveled a couple of light-days, and the Voyagers have barely logged a dozen light-hours.

Fermi estimation problem for anthropologists: Which is more likely to have struck and killed someone: A random Oldowan stone tool, a random Voyager spacecraft, or a random 77 Plymouth Voyager? I'm guessing it's not the middle one. (Unless there was an accident during assembly.)

Measured relative to the Earth

By this measure, the Ethiopian stone tools win again. They were crafted relatively close to the Equator, so they've spent their millions of years traveling at about 460 meters per second as the Earth rotates, racking up 4 light-years on their odometers.

Speed over the Earth's surface

This rotating frame of reference effectively zeroes out the odometer on the stone tools. It also means that spacecraft far away from the Earth are sort of a weird case, since they "move" over the Earth's surface at the speed at which the planet spins. But that turns out not to matter, because the winner in this category is Vanguard 1, which has been in orbit since 1958, logging about 8.888 billion kilometers over the surface.

Normal speed, without any weird space stuff or Earth rotation or whatever

First, let's think about things that travel in a straight line. There are a lot of those, including a 1966 Volvo in Long Island which has driven 3 million miles. There are other vehicles that travel long distances—long-haul airliners, for example—but the winner in this category might actually be a human.

United Airlines flight attendant Ron Akana traveled about 20 million miles over his 63-year career, which might be the most of any human; even someone who sailed on steamships their whole life would have a hard time traveling that far.^{[It's not enough to beat the astronauts, though; cosmonaut Valeri Polyakov spent over a year in orbit, which adds up to a life odometer 10 times longer than Ron Akana's.]}​^{[You could argue that he doesn't qualify as a human-made object, but he was certainly made. And anyway, he may have an object he carried with him for most of those flights. The article mentions he was married, so perhaps his wedding ring qualifies.]}

Some train cars—or things used in trains—might push the total a little higher, but it seems unlikely that any kind of vehicle has traveled 100 million miles.

Things that rotate are a different matter.

We'll start with hard drive platters.^{[If you're reading this in the future, hard drive platters were these things that ... oh, never mind, it's not important.]} A 3.5" hard drive at 7200 rpm is moving at about 80 mph. Drives have a limited lifetime—especially if they're run constantly—but it's easy to imagine the edge of a platter somewhere logging millions of miles before it died.

The energy industry has some good candidates. The tips of wind turbines can move faster than cars, and turbines can run for decades. Even if the wind isn't constant, some of them have probably traveled tens of millions of miles.

The discs used in flywheel energy storage are even more promising than wind turbines. Flywheels are designed to spin (usually in a vacuum) for decades at a time, with rotor speeds above Mach 1. There's probably a flywheel somewhere whose rotor rim has traveled a nine-digit number of miles.^{[Hundreds of millions.]}

The edges of centrifuges, especially those used for uranium enrichment, can travel even faster—in fact, they push the very limits of how fast material can rotate.

There's an absolute limit to how fast anything can spin without breaking apart. For the very strongest materials, like carbon fiber and kevlar, the top speed that the outer edge of a spinning cylinder can travel is between 1 and 2 kilometers per second.^{[Units are weird: The maximum speed the edge of a cylinder of a given material can rotate is equal to the square root of its specific tensile strength (tensile strength over density).]} If we assume those materials and the precision techniques to produce them have only existed for the last half-century, then the greatest distance a centrifuge could possibly have traveled is about a billion kilometers—and the actual record is almost certainly much less. This is why uranium enrichment involves titanium centrifuges; the uranium needs to be spun very fast, and only specialized materials are strong enough to hold together at those speeds.

All in all, uranium enrichment centrifuges seem like a likely winner, with total lifetime odometer that might push into the hundreds of millions of miles.

How fast?

So, exactly how far has the longest-operating centrifuge traveled?

¯\(°_o)/¯

I don't know.

Normally I don't give up like this, but if I had a way to estimate exactly how fast and for how long the labs in different countries have been spinning their uranium enrichment centrifuges, I would probably not be blogging about it here.

I also have many facts about meteors, tornadoes, and ice.

In any case, the centrifuges have logged far less total distance than many manmade objects, including (by various measures) the Ethiopian stone tools, the ISS, Mariner 10, and the Voyagers.

And for what it's worth, based on the "every 3,000 miles" rule, the Voyagers have missed several million oil changes each.

That's totally an industry scam. NASA shouldn't change Voyager's oil more than every 5 or 6 thousand miles.

Maybe it's best that we just leave them.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Enforced by Radar

I've occasionally seen "radar enforced" on speed limit signs, and I can't help but ask: How intense would radio waves have to be to stop a car from going over the speed limit, and what would happen if this were attempted?

—joausc

Radio waves exert force on things.

Not a lot of force. The average cell phone transmitter exerts about a billionth of a newton of pressure on its surroundings. That means that it would take several trillion cell phones to collectively levitate a snowflake; the pressure from one phone wouldn't even measurably slow it down.

Under the right circumstances, the convection from the phone's heat could probably deflect a snowflake.

If the phone did put out enough energy to levitate a snowflake by radiation pressure, the power flowing through the snowflake (a few kilowatts) would quickly cause the snowflake to become a raindrop, which would quickly become water vapor, which would quickly become the least of your problems.

I thought our plan had unlimited snowflake levitation.

The fate of the snowflake hints at what kinds of problems our car will encounter.

If you want to slow down a one-ton car by radiation pressure, your radar gun would need to deliver about two trillion joules worth of radiation—the energy of a small nuclear weapon.^{[The formula for figuring out that amount out is simple: The energy required is equal to the desired change in speed (say, 20 mph) times the mass of the car times the speed of light.]} The radar gun would need to emit even more energy than that, since not all of the radiation will be absorbed (or reflected) by the car.^{[The fact that some of it is reflected makes things easier, since that doubles the momentum delivered by the radiation. This is why simple solar sails are white and not black. For more on radar reflectivity of materials, you can check out one of the worst scanned PDFs I've ever seen.]}

Your radar gun would also vaporize the car. This is a problem, in one sense, but it's also a solution. Even if most of the energy is reflected, the portion that was absorbed would convert the materials in the car into gas or plasma. The expanding cloud would exert a lot more pressure on the car than the radiation itself.^{[This process, called ablation, is also what got rid of the Moon in the What If #13.]} This is convenient—it means that we wouldn't need nearly as much energy to stop the car as we would using radiation pressure alone.

There are even simpler ways to slow down a car with radiation. For example, you could aim a radiation beam at the tires and melt them, or use the electromagnetic radiation to knock out the car's electrical systems. Or just use a laser pointer to blind the driver and hope they reflexively slow down.

Of course, you don't need any of those things. If your goal is to slow down the car—rather than to catch speeders—your radar gun doesn't need any power. You can just stand by the side of the road next to a police car holding a fake radar gun.

He's been waiting his whole life for someone to ask "what's your sign", but nobody has.

In the end, a radar gun capable of slowing cars through radiation pressure would be roughly equivalent to a nuclear weapon, and using nuclear strikes in response to traffic violations is probably overkill. It would work, in the literal sense, but it would also destroy the offender, car, police officer, road, and all other traffic for miles around.^{[It would also cause fragments of the driver to violate the speed limit in all directions at once.]}

Of course, maybe using the apocalyptic radar gun wouldn't be necessary; just the threat of a nuclear strike against drivers would probably deter speeding.

Come to think of it, maybe that's what those other signs you sometimes see are hinting at.

Protip for potential speeders: Since the B-2's stealth technology incorporates radar-absorbing materials, it's particularly vulnerable to radar gun death rays.

we almost split

Soda Sequestration

How much CO₂ is contained in the world's stock of bottled fizzy drinks? How much soda would be needed to bring atmospheric CO₂ back to preindustrial levels?

Brandon Seah

For most of the history of civilization, there were about 270 parts per million of carbon dioxide in the atmosphere. In the last hundred years, industrial activity has pushed that number up to 400 parts per million.

One "part per million" of CO₂ weighs about 7.8 billion tons. A can of soda contains in the neighborhood of 2.2 grams of CO₂, so you would need about 450 quadrillion cans of soda. That's enough to cover the Earth's land with ten layers of cans.

Mesosphere, asthenosphere, lithosphere, sodasphere

There's clearly not enough room to do this. Even if we stacked the cans up to the edge of space,^{[I don't have any hard numbers, but my guess would be that you could probably stack supermarket soda six-pack crates a few hundred meters high before the bottom layer ruptures.]} they'd still take up an area the size of Rhode Island.^{[We shouldn't actually try it, given what happened last time.]}

We'd need to add even more cans to keep up with ongoing emissions. We're currently increasing the atmosphere's CO₂ concentration by an average of 2 parts per million each year:

If you squint at some of these graphs, you can see the effect of the fall of the Soviet Union due to abrupt industrial and land use changes.

At that rate, we'd need to add one can of soda per person every 30 seconds, which is about 10,000 times the current consumption rate.^{[The global average is one can per person every 5 days. In the US, the average is one every 18 hours.]} That would add a new layer of cans to the ground every 6^{[I originally had the wrong number here; thank you to Paulina for catching it!]} years or so.

This layer of cans would get pretty annoying.

Following the resurfacing, that soda/coke/pop dialect map will come to define our national political divisions.

Are there any ways out of this predicament?

In some areas, you can turn in soda cans for recycling and receive a small amount of money; in Massachusetts, where I live, it's 5 cents. If you collected one year's worth of soda cans—instead of layering them across the Earth's surface—and emptied them out, you could redeem them for $372 trillion.

With that much money, you could simply buy the world's current reserves^{[Source: xkcd.com/980, bottom right.]} of coal, oil, and natural gas—the source of the whole problem.

Then, you put it all back in the ground and leave it there.

You're never, ever gonna get your wish.

Problem solved.

you are awesome, the most beautiful person i have ever met and you make me happy everyday i spend with you

Tungsten Countertop

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

Michael Leuchtenburg

Not very far.

With its high melting point, tungsten is a good^{[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.

Assuming it's ever launched, Solar Probe Plus will get within 1/8th of Mercury's orbital distance.

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.^{["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.^{[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^{[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.^{[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.

Goodbye, faithful countertop. I'm not sure what your mission was, but I'm sure you've performed it well.

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.

Close enough.

i'm finishing this text in koh kong, you are lying in front of me, reading your book. we came back yesterday from our adventure in the montains brought back by the red cross. we went to the market this morning to try out things (fried bananas and cane juice). i feel filled with you. you are beautiful. i love you.