Biologists use a number called the “inbreeding coefficient” to quantify the percentage of someone’s chromosomes that are likely to be identical. A child from unrelated parents has an inbreeding coefficient of 0, while one who has a completely duplicated set of chromosomes has an inbreeding coefficient of 1.
This brings us to the answer to the original question. A child from a parent who self-fertilized would be like a clone of the parent with severe genetic damage. The parent would have all the genes the child would, but the child wouldn’t have all the genes of the parent. Half the child’s chromosomes would have their “partner” chromosomes replaced by a copy of themselves.
This means the child would have an inbreeding coefficient of 0.50. This is very high; it’s what you would expect in a child of three generations of consecutive sibling marriages. According to D. S. Falconer’s Introduction to Quantitative Genetics, an inbreeding coefficient of 0.50 would result in an average of a 22-point reduction in IQ and a 4-inch reduction in height at age ten. There would be a very good chance that the resulting fetus would not survive to birth.
This kind of inbreeding was famously exhibited by royal families attempting to keep their bloodlines “pure.” The European House of Hapsburg, a family of European rulers from the mid-second millennium, was marked by frequent cousin marriages, culminating in the birth of King Charles II of Spain.
Charles had an inbreeding coefficient of 0.254, making him slightly more inbred than a child of two siblings (0.250). He suffered from extensive physical and emotional disabilities, and was a strange (and largely ineffective) king. In one incident, he reportedly ordered that the corpses of his relatives be dug up so he could look at them. His inability to bear children marked the end of that royal bloodline.
Self-fertilization is a risky strategy, which is why sex is so popular among large and complex organisms.3 There are occasionally complex animals that reproduce asexually,4 but this behavior is relatively rare. It typically appears in environments where it’s difficult to reproduce sexually, whether due to resource scarcity, population isolation . . .
Life finds a way.
. . . or overconfident theme park operators.
1Because 1 is the multiplicative identity.
2Some forms of SMA are actually caused by a defect in two genes, so in practice the statistical picture is a little more complicated.
3Well, one of the reasons.
4“Tremblay’s Salamander” is a hybrid species of salamander that reproduces exclusively by self-fertilizing. These salamanders are an all-female species, and — strangely — have three genomes instead of two. To breed, they go through a courtship ritual with male salamanders of related species, then lay self-fertilized eggs. The male salamander gets nothing out of it; he’s simply used to stimulate egg-laying.
High Throw
Q. How high can a human throw something?
—Irish Dave on the Isle of Man
A. Humans are good at throwing things. In fact, we’re great at it; no other animal can throw stuff like we can.
It’s true that chimpanzees hurl feces (and, on rare occasions, stones), but they’re not nearly as accurate or precise as humans. Antlions throw sand, but they don’t aim it. Archerfish hunt insects by throwing water droplets, but they use specialized mouths instead of arms. Horned lizards shoot jets of blood from their eyes for distances of up to 5 feet. I don’t know why they do this because whenever I reach the phrase “shoot jets of blood from their eyes” in an article I just stop there and stare at it until I need to lie down.
So while there are other animals that use projectiles, we’re just about the only animal that can grab a random object and reliably nail a target. In fact, we’re so good at it that some researchers have suggested that rock-throwing played a central role in the evolution of the modern human brain.
Throwing is hard.1 In order to deliver a baseball to a batter, a pitcher has to release the ball at exactly the right point in the throw. A timing error of half a millisecond in either direction is enough to cause the ball to miss the strike zone.
To put that in perspective, it takes about five milliseconds for the fastest nerve impulse to travel the length of the arm. That means that when your arm is still rotating toward the correct position, the signal to release the ball is already at your wrist. In terms of timing, this is like a drummer dropping a drumstick from the tenth story and hitting a drum on the ground on the correct beat.
We seem to be much better at throwing things forward than throwing them upward.2 Since we’re going for maximum height, we could use projectiles that curve upward when you throw them forward; the Aerobie Orbiters I had when I was a kid often got stuck in the highest treetops.3 But we could also sidestep the whole problem by using a device like this one:
A mechanism for hitting yourself in the head with a baseball after a four-second delay
We could use a springboard, a greased chute, or even a dangling sling—anything that redirects the object upward without adding to or subtracting from its speed. Of course, we could also try this:
I ran through the basic aerodynamic calculations for a baseball thrown at various speeds. I will give these heights in units of giraffes:
The average person can probably throw a baseball at least three giraffes high:
Someone with a reasonably good arm could manage five:
A pitcher with an 80 mph fastball could manage ten giraffes:
Aroldis Chapman, the holder of the world record for fastest recorded pitch (105 mph), could in theory launch a baseball 14 giraffes high:
But what about projectiles other than a baseball? Obviously, with the aid of tools like slings, crossbows, or the curved xistera scoops in jai alai, we can launch projectiles much faster than that. But for this question, let’s assume we stick to bare-handed throwing.
A baseball is probably not the ideal projectile, but it’s hard to find speed data on other kinds of thrown objects. Fortunately, a British javelin thrower named Roald Bradstock held a “random object throwing competition,” in which he threw everything from dead fish to an actual kitchen sink. Bradstock’s experience gives us a lot of useful data.4 In particular, it suggests a potentially superior projectile: a golf ball.
Few professional athletes have been recorded throwing golf balls. Fortunately, Bradstock has, and he claims a record throw of 170 yards. This involved a running start, but even so, it’s reason to think that a golf ball might work better than a baseball. From a physics standpoint, it makes sense; the limiting factor in baseball pitches is the torque on the elbow, and the lighter golf ball might allow the pitching arm to move slightly faster.
The speed improvement from using a golf ball instead of a baseball would probably not be very large, but it seems plausible that a professional pitcher with some time to practice could throw a golf ball faster than a baseball.
If so, based on aerodynamic calculations, Aroldis Chapman could probably throw a golf ball about sixteen giraffes high:
This is probably about the maximum possible altitude for a thrown object.
. . . unless you count the technique by which any five-year-old can beat all these records easily.
1Citation: my Little League career.
2Counterexample: my Little League career.
3Where they remained forever.
4And a lot of other data, too.
Lethal Neutrinos
Q. How close would you have to be to a supernova to get a lethal dose of neutrino radiation?
—Dr. Donald Spector
A. 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 ph
ysics 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.
Okay, you can stop looking at your hand now.
The reason you don’t notice the neutrino flood is that neutrinos mostly ignore ordinary matter. On average, out of that massive flood, only one neutrino will “hit” an atom in your body every few years.1
In fact, neutrinos are so shadowy that the entire Earth is transparent to them; nearly all of the Sun’s neutrino steam goes straight through it unaffected. To detect neutrinos, people build giant tanks filled with hundreds of tons of target 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!
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.”2 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—it’s that you can’t imagine a situation where it would apply.3
Similarly, it’s hard to produce enough neutrinos to get even a single one of them to interact with matter; it’s strange to imagine a scenario in which there’d be enough of them to hurt you.
Supernovae provide that scenario.4 Dr. Spector, the Hobart and William Smith Colleges physicist who asked me this question, 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:
A supernova, seen from as far away as the Sun is from the Earth, or the detonation of a hydrogen bomb pressed against your eyeball?
Can you hurry up and set it off? This is heavy.
Applying Dr. Spector’s 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. 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 1 parsec5 would be around half a nanosievert, or 1/500th the dose from eating a banana.6
A fatal radiation dose is about 4 sieverts. Using the inverse-square law, we can calculate the radiation dose:
That’s 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 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.
1Less often if you’re a child, since you have fewer atoms to be hit. Statistically, your first neutrino interaction probably happens somewhere around age ten.
2Which would still be less than 1 percent of the ants in the world.
3If 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.
4“Supernovas” is also fine. “Supernovii” is discouraged.
53.262 light-years, or a little less than the distance from here to Alpha Centauri.
6“Radiation Dose Chart,” http://xkcd.com/radiation.
weird (and worrying) questions from the what if? INBOX, #8
Q. A toxin blocks the ability of the nephron tubule reabsorption but does not affect filtration. What are the possible short-term effects of this toxin?
—Mary
Q. If a Venus fly trap could eat a person, about how long would it take for the human to be fully de-juiced and absorbed?
—Jonathan Wang
Speed Bump
Q. How fast can you hit a speed bump while driving and live?
—Myrlin Barber
A. Surprisingly fast.
First, a disclaimer. After reading this answer, don’t try to drive over speed bumps at high speeds. Here are some reasons:
You could hit and kill someone.
It can destroy your tires, suspension, and potentially your entire car.
Have you read any of the other answers in this book?
If that’s not enough, here are some quotes from medical journals on spinal injury from speed bumps.
Examination of the thoracolumbar X-ray and computed tomography displayed compression fractures in four patients . . . Posterior instrumentation was applied . . . All patients recovered well except for the one with cervical fracture.
L1 was the most frequently fractured vertebra (23 /52, 44.2 percent).
Incorporation of the buttocks with realistic properties diminished the first vertical natural frequency from ~12 to 5.5 Hz, in agreement with the literature.
(That last one isn’t directly related to speed bump injuries, but I wanted to include it anyway.)
Regular little speed bumps probably won’t kill you
Speed bumps are designed to make drivers slow down. Going over a typical speed bump at 5 miles per hour results in a gentle bounce,1 while hitting one at 20 delivers a sizable jolt. It’s natural to assume that hitting a speed bump at 60 would deliver a proportionally larger jolt, but it probably wouldn’t.
As those medical quotes attest, it’s true that people are occasionally injured by speed bumps. However, nearly all of those injuries happen to a very specific category of people: those sitting in hard seats in the backs of buses, riding on poorly maintained roads.
When you’re driving a car, the two main things protecting you from bumps in the road are the tires and the suspension. No matter how fast you hit a speed bump, unless the bump is large enough to hit the frame of the car, enough of the jolt will be absorbed by these two systems that you probably won’t be hurt.
Absorbing the shock won’t necessarily be good for those systems. In the case of the tires, they may absorb it by exploding.2 If the bump is large enough to hit the wheel rims, it may permanently damage a lot of important parts of the car.
The typical speed bump is between 3 and 4 inches tall. That’s also about how thick an average tire’s cushion is (the separation between the bottom of the rims and the ground).3 This means that if a car hits a small speed bump, the rim won’t actually touch the bump; the tire will just be compressed.
The typical sedan has a top speed of around 120 miles per hour. Hitting a speed bump at that speed would, in one way or another, probably result in losing control of the car and crashing.4 However,
the jolt itself probably wouldn’t be fatal.
If you hit a larger speed bump—like a speed hump or speed table—your car might not fare so well.
How fast would you have to go to definitely die?
Let’s consider what would happen if a car were going faster than its top speed. The average modern car is limited to a top speed of around 120 mph, and the fastest can go about 200.
While most passenger cars have some kind of artificial speed limits imposed by the engine computer, the ultimate physical limit to a car’s top speed comes from air resistance. This type of drag increases with the square of speed; at some point, a car doesn’t have enough engine power to push through the air any faster.
If you did force a sedan to go faster than its top speed—perhaps by reusing the magical accelerator from the relativistic baseball—the speed bump would be the least of your problems.
Cars generate lift. The air flowing around a car exerts all kinds of forces on it.
Where did all these arrows come from?
The lift forces are relatively minor at normal highway speeds, but at higher speeds they become substantial.
In a Formula One car equipped with airfoils, this force pushes downward, holding the car against the track. In a sedan, they lift it up.
Among NASCAR fans, there’s frequently talk of a 200-mph “liftoff speed” if the car starts to spin. Other branches of auto racing have seen spectacular backflip crashes when the aerodynamics don’t work out as planned.
What If? Page 13