To test this theory, I sent this picture to my mother and asked her what she thought had happened. She immediately replied,2 “The kid knocked over the vase and the cat is investigating.”
She cleverly rejected alternate hypotheses, including:
The cat knocked over the vase.
The cat jumped out of the vase at the kid.
The kid was being chased by the cat and tried to climb up the dresser with a rope to escape.
There’s a wild cat in the house, and someone threw a vase at it.
The cat was mummified in the vase, but arose when the kid touched it with a magic rope.
The rope holding the vase broke and the cat is trying to put it back together.
The vase exploded, attracting a child and a cat. The child put on the hat for protection from future explosions.
The kid and cat are running around trying to catch a snake. The kid finally caught it and tied a knot in it.
All the computers in the world couldn’t figure out the correct answer faster than any one parent could. But that’s because computers haven’t been programmed to figure that kind of thing out,3 whereas brains have been trained by millions of years of evolution to be good at figuring out what other brains around them are doing and why.
So we could choose a task to give the humans an advantage, but that’s no fun; computers are limited by our ability to program them, so we’ve got a built-in advantage.
Instead, let’s see how we compete on their turf.
The complexity of microchips
Rather than making up a new task, we’ll simply apply the same benchmark tests to humans that we do to computers. These usually consist of things like floating point math, saving and recalling numbers, manipulating strings of letters, and basic logical calculations.
According to computer scientist Hans Moravec, a human running through computer chip benchmark calculations by hand, using pencil and paper, can carry out the equivalent of one full instruction every minute and a half.4
By this measure, the processor in a midrange mobile phone could do calculations about 70 times faster than the entire world population. A new high-end desktop PC chip would increase that ratio to 1500.
So, what year did a single typical desktop computer surpass the combined processing power of humanity?
1994.
In 1992, the world population was 5.5 billion people, which means their combined computing power by our benchmark test was about 65 MIPS (million instructions per second).
That same year, Intel released the popular 486DX, which in its default configuration achieved about 55 or 60 MIPS. By 1994, Intel’s new Pentium chips were achieving benchmark scores in the 70s and 80s, leaving humanity in the dust.
You might argue that we’re being a little unfair to the computers. After all, these comparisons are one computer against all humans. How do all humans stack up against all computers?
This is tough to calculate. We can easily come up with benchmark scores for various types of computers, but how do you measure the instructions per second of, say, the chip in a Furby?
Most of the transistors in the world are in microchips not designed to run these tests. If we’re assuming that all humans are being modified (trained) to carry out the benchmark calculations, how much effort should we spend to modify each computer chip so it can run the benchmark?
To avoid this problem, we can instead estimate the aggregate power of all the world’s computing devices by counting transistors. It turns out that processors from the 1980s and processors from today have a roughly similar ratio of transistors to MIPS—about 30 transistors per instruction per second, give or take an order of magnitude.
A paper by Gordon Moore (of Moore’s law fame) gives figures for the total number of transistors manufactured per year since the 1950s. It looks something like this:
Using our ratio, we can convert the number of transistors to a total amount of computing power. This tells us that a typical modern laptop, which has a benchmark score in the tens of thousands of MIPS, has more computing power than existed in the entire world in 1965. By that measure, the year when the combined power of computers finally pulled ahead of the combined computing power of humans was 1977.
The complexity of neurons
Again, making people do pencil-and-paper CPU benchmarks is a phenomenally silly way to measure human computing power. Measured by complexity, our brains are more sophisticated than any supercomputer. Right?
Right. Mostly.
There are projects that attempt to use supercomputers to fully simulate a brain at the level of individual synapses.5 If we look at how many processors and how much time these simulations require, we can come up with a figure for the number of transistors required to equal the complexity of the human brain.
The numbers from a 2013 run of the Japanese K supercomputer suggest a figure of 1015 transistors per human brain.6 By this measure, it wasn’t until the year 1988 that all the logic circuits in the world added up to the complexity of a single brain . . . and the total complexity of all our circuits is still dwarfed by the total complexity of all brains. Under Moore’s law–based projections, and using these simulation figures, computers won’t pull ahead of humans until the year 2036.7
Why this is ridiculous
These two ways of benchmarking the brain represent opposite ends of a spectrum.
One, the pencil-and-paper Dhrystone benchmark, asks humans to manually simulate individual operations on a computer chip, and finds humans perform about 0.01 MIPS.
The other, the supercomputer neuron simulation project, asks computers to simulate individual neurons firing in a human brain, and finds humans perform about the equivalent of 50,000,000,000 MIPS.
A slightly better approach might be to combine the two estimates. This actually makes a strange sort of sense. If we assume our computer programs are about as inefficient at simulating human brain activity as human brains are at simulating computer chip activity, then maybe a more fair brain power rating would be the geometric mean of the two numbers.
The combined figure suggests human brains clock in at about 30,000 MIPS—right about on par with the computer on which I’m typing these words. It also suggests that the year when Earth’s digital complexity overtook its human neurological complexity was 2004.
Ants
In his paper “Moore’s Law at 40,” Gordon Moore makes an interesting observation. He points out that, according to biologist E. O. Wilson, there are 1015 to 1016 ants in the world. By comparison, in 2014 there were about 1020 transistors in the world, or tens of thousands of transistors per ant.8
An ant’s brain might contain a quarter of a million neurons, and thousands of synapses per neuron, which suggests that the world’s ant brains have a combined complexity similar to that of the world’s human brains.
So we shouldn’t worry too much about when computers will catch up with us in complexity. After all, we’ve caught up to ants, and they don’t seem too concerned. Sure, we seem like we’ve taken over the planet, but if I had to bet on which one of us would still be around in a million years—primates, computers, or ants—I know who I’d pick.
1Except Red Delicious apples, whose misleading name is a travesty.
2Our house had a lot of vases when I was a kid.
3Yet.
4This figure comes from a list (http://www.frc.ri.cmu.edu/users/hpm/book97/ch3/processor.list.txt) in Hans Moravec’s book Robot: Mere Machine to Transcendent Mind.
5Although even this might not capture everything that’s going on. Biology is tricky.
6Using 82,944 processors with about 750 million transistors each, K spent 40 minutes simulating one second of brain activity in a brain with 1 percent of the number of
connections as a human’s.
7If it’s past the year 2036 right now while you’re reading this, hello from the distant past! I hope things are better in the future. P.S. Please figure out a way to come get us.
8“TPA.”
Little Planet
Q. If an asteroid was very small but supermassive, could you really live on it like the Little Prince?
—Samantha Harper
“Did you eat my rose?” “Maybe.”
A. 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.1 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.
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 visible only as points of light. In fact, that’s where their name comes from—the word asteroid means “starlike.”
We got our first confirmation of what asteroids looked like in 1971, when Mariner 9 visited Mars and snapped pictures of Phobos and Deimos. These moons, believed to be captured asteroids, solidified the modern image of asteroids as cratered potatoes.
Before the 1970s, it was common for science fiction to assume small asteroids would be round, like planets.
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.
Rather than using science to chip away at the story, let’s see what strange new pieces it can add. If there really were a superdense asteroid with enough surface gravity to walk around on, it would have some pretty remarkable properties.
If the asteroid had a radius of 1.75 meters, then in order to have Earthlike 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.
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 this asteroid by jumping.
However, the weird thing about escape velocity is that it doesn’t matter which direction you’re going.2 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.
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.
But this would be a weird orbit.
Tidal forces would act on you in several ways. If you stretched your arm down toward the planet, it would be pulled much harder than the rest of you. And when 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.3 This wouldn’t happen to you. However, your orbit would become chaotic and unstable.
These types of orbits were investigated in a paper by Radu D. Rugescu and Daniele Mortari. Their simulations showed that large, elongated objects follow strange paths around their central bodies. Even their centers of mass don’t move in the traditional ellipses; some adopt pentagonal orbits, while others tumble chaotically and crash into the planet.
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 a challenge for such a 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 entering orbit, 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 the Prince’s decision to sign with the Miami Heat.
1Although not everyone sees it this way. Mallory Ortberg, writing on the-toast.net, characterized the story of The Little Prince as a wealthy child demanding that a plane crash survivor draw him pictures, then critiquing his drawing style.
2. . . 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 unexpectedly significant here.
3This is presumably what happened to Sonic the Hedgehog.
Steak Drop
Q. From what height would you need to drop a steak for it to be cooked when it hit the ground?
—Alex Lahey
A. I hope you like your steaks Pittsburgh Rare. And you may need to defrost it after you pick it up.
Things get really hot when they come back from space. As they enter the atmosphere, the air can’t move out of the way fast enough, and gets squished in front of the object—and compressing air heats it up. As a rule of thumb, you start to notice compressive heating above about Mach 2 (which is why the Concorde had heat-resistant material on the leading edge of its wings).
When skydiver Felix Baumgartner jumped from 39 kilometers, he hit Mach 1 at around 30 kilometers. This was enough to heat the air by a few degrees, but the air was so far below freezing that it didn’t make a difference. (Early in his jump, it was about minus 40 degrees, which is that magical point where you don’t have to clarify whether you mean Fahrenheit or Celsius—it’s the same in both.)
As far as I know, this steak question originally came up in a lengthy 4chan thread, which quickly disintegrated into poorly informed physics tirades intermixed with homophobic slurs. There was no clear conclusion.
To try to get a better answer, I decided to run a series of simulations of a steak falling from various heights.
An 8-ounce steak is about the size and shape of a hockey puck, so I based my steak’s drag coefficients on those given on page 74 of The Physics of Hockey (which author Alain Haché actually measured personally using some lab equipment). A steak isn’t a hockey puck, but the precise drag coefficient turned out not to make a big difference in the result.
Since answering these questions often includes analyzing unusual objects in extreme physical circumstances, often the only relevant research I can find is US military studies from the Cold War era. (Apparently, the US government was shoveling tons of money at anything even loosely related to weapons research.) To get an idea of how the air would heat the steak, I looked at research papers on the heating of ICBM nose cones as they reenter the atmosphere. Two of the most useful were “Predictions of Aerodynamic Heating on Tactical Missile Domes” and “Calculation of Reentry-Vehicle Temperature History.”
Lastly, I had to figure out exactly how quickly heat spreads through a steak. I started by looking at some papers from industrial food production that simulated heat
flow through various pieces of meat. It took me a while to realize there was a much easier way to learn what combinations of time and temperature will effectively heat the various layers of a steak: Check a cookbook.
Jeff Potter’s excellent book Cooking for Geeks provides a great introduction to the science of cooking meat, and explains what ranges of heat produce what effects in steak and why. Cook’s The Science of Good Cooking was also helpful.
Putting it all together, I found that the steak will accelerate quickly until it reaches an altitude of about 30–50 kilometers, at which point the air gets thick enough to start slowing it back down.
The falling steak’s speed would steadily drop as the air gets thicker. No matter how fast it was going when it reached the lower layers of the atmosphere, it would quickly slow down to terminal velocity. No matter the starting height, it always takes six or seven minutes to drop from 25 kilometers to the ground.
For much of those 25 kilometers, the air temperature is below freezing—which means the steak will spend six or seven minutes subjected to a relentless blast of subzero, hurricane-force winds. Even if it’s cooked by the fall, you’ll probably have to defrost it when it lands.
When the steak does finally hit the ground, it will be traveling at terminal velocity—about 30 meters per second. To get an idea of what this means, imagine a steak flung at the ground by a major-league pitcher. If the steak is even partially frozen, it could easily shatter. However, if it lands in the water, mud, or leaves, it will probably be fine.1
What If? Page 8