by Tom Rogers
Apologists for A.I. often say that the narrator in the opening scenes is not to be taken literally. What he really means is that the robots can go for extremely long periods of time without being recharged, refueled, or rebuilt. These lengthy time spans make it seem as though robots need no resources beyond those used to create them.
Ten years between refueling is about the shortest time that would give the illusion of robots needing no outside resources. So let’s see how much energy storage would be needed. Gasoline is used for energy storage in automobiles not just because it’s available but because it has one of the best energy to mass ratios of any energy storage medium currently available. It seems like a good starting point. As mentioned earlier, a typical male human requires about 2,000 kilocalories of food energy per day just to stay alive; if he performs manual labor, he needs about 2,500 kilocalories. Assume the human is replaced with a 100 percent efficient gasoline-powered robot. A ten-year fuel supply would require 1,900 pounds (864 kg) of gasoline. Obviously, no humansized robot is going to be walking around with that much fuel aboard, let alone be 100 percent efficient. To be viable as a tenyear energy supply, a storage medium would have to contain about one hundred times more energy per pound than gasoline— fat chance.
The only solution would be to use some type of nuclear fuel. Needless to say, this has all kinds of problems: radioactivity, for one. Certainly, the movie’s scene in which obsolete robots are destroyed in sick ways to entertain a cheering circus-like throng could never be done.The crowd would be irradiated from leftover fuel and nuclear waste inside the robots.
Nuclear fuel produces heat, which then has to be converted to electrical energy in order to be useful inside a robot. There’s no known mechanism for producing electricity directly from nuclear fuel.The second law says that only a fraction of the heat produced by the nuclear fuel will actually end up as electrical energy. The rest has to be dumped into the environment as waste heat. To get any appreciable amount of efficiency, the heat converted to energy has to be produced at an elevated temperature, probably at least 932 degrees Fahrenheit (500°C). Aside from being radiation hazards, the robots would likely be fire hazards.
The movie’s main character—a robot that looks like a little boy— becomes depressed because his adopted human mother doesn’t love him. At the end of his emotional rope, he jumps into salt water in a suicide attempt. He’s rescued, but before he can dry off he ends up piloting a helicopter-turned-submarine to the bottom of the ocean where he accidentally becomes trapped. When rescued—a mere 2,000 years later—he functions like he’d been on the bottom a few minutes. Not even his t-shirt has deteriorated. Park a car for two years, turn the ignition key, and you’ll be lucky if it sputters.
Obviously, the moviemakers took the opening narrator pretty seriously. A 2,000-year supply of nuclear fuel for the hypothetical 160-pound bedridden human described earlier would add up to the energy equivalent of 1.4 kilotons of TNT. This is like a lowyield tactical nuclear device that could take out a neighborhood. Even if the child robot had half as much, combine his stored energy with 2,000 years of neglect and he’d be a walking Chernobyl waiting for meltdown.
A.I. seems to be a movie that wants to make serious statements about the nature of love and the mother-child relationship, yet, from a physics standpoint, achieves pure silliness. Its violations of the first and second laws are not consistent with its serious tone and are unforgivable.
It’s easy to obey the first and second laws, especially in movies with serious science fiction themes. If it’s not done, the movie becomes, at best, a science fantasy or cinematic comic book. At worst, the movie turns into pure nonsense.
Summary of Movie Physics Rating Rubrics
The following is a summary of the key points discussed in this chapter that affect a movie’s physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best.
[–] [–] [–] Serious violations of the first law. Includes the metamorphosis of creatures into a very large size with no apparent source of matter or reduction in density.
[–] [–] [–] Depictions of perpetual motion machines.
[–] [–] [–] Depictions of superhuman robots that never need recharging, refueling, or rebuilding. At best this categorizes a film as a cinematic comic book.
[–] [–] Minor violations of the first or second laws that are not significant parts of the story line or plot.
[+] [+] Depicting robots that break down and regularly need to be refueled or recharged.
CHAPTER 4
SCALING PROBLEMS:
Big Bugs and Little People
It’s an old movie gimmick: radioactive contamination, toxic waste, genetic engineering, or some other out-of-control technology abnormally shrinks or expands someone or some creature. While the gimmick is certainly entertaining, the physics are flaky.
SCALING DOWN HUMANS
In Honey I Shrunk the Kids [NR] (1989), Rick Moranis plays a whacky inventor named Wayne Szalinski who works at home and successfully builds a device for miniaturizing objects. Naturally, his son, daughter, and two neighbor kids end up accidentally (surprise, surprise) getting shrunk. After Szalinski unknowingly sweeps them up and throws them out, they must journey across the foreboding backyard to get back to the house. Who would have guessed that hanging around the backyard could be such an adventure?
Ordinary matter is almost entirely filled with empty space. The vast majority of mass in an atom is contained in its nucleus. The mass of its electrons is inconsequential by comparison. On an atomic level, there are huge distances between the nucleus of an atom and the nuclei of its nearest neighbors, even in a solid. Other than containing a few small specks, namely electrons, the space between nuclei is filled with essentially nothing. It is not filled with air, it’s filled with void.
It’s conceivable that people could be shrunk by somehow removing some of the empty space inside them. This happens in a black hole, although to a much more dramatic extent. Of course, there are many problems associated with squeezing empty space out of matter. For example, the repulsion forces between nearby atoms would increase to levels much higher than normal, making it extremely hard to keep the atoms from moving apart— explosively. However, let’s ignore the problems and assume the space can be magically removed. Using this system, a 100-pound teenager reduced to the size of an ant would still have exactly the same number of atoms in her body. This means she would have exactly the same amount of mass and weight.
When something is scaled up, all its dimensions are multiplied by the scaling factor. When scaled down, all its dimensions are divided by the scaling factor. Note that any area on any object will scale up and down with the square of the scaling factor. For example, scale a human up by a factor of 10, and the area under her feet will increase by a factor of 102, or 100. Scale her down by a factor of 10, and the area under her feet will scale down by a factor of 100 or become 1/100 its original size.
Let’s assume Szalinski’s teenage daughter’s foot is about 10 inches (25.4 cm) long by 4 inches (10.2) wide, giving an area of 40 square inches. When walking or running, her weight would momentarily be applied to the area of a single foot. This yields a pressure as follows:
Pressure = weight/area
= 100 lbs/40 sq inches
= 2.5 psi or 0.18 atm
If the teenager is scaled down by a factor of 100, her foot will now be 0.1 inches long by 0.04 inches wide for an area of 0.004 square inches. This increases the pressure beneath her feet by a factor of 10,000. If she places her weight on one foot, the pressure would equal 25,000 pounds per square inch. Standing on both feet, the pressure would be 12,500 pounds per square inch. Either of these pressures would easily exceed the compressive strength of concrete (typically 3,000 to 4,000 psi). But wal
king on a concrete surface might break her feet before it broke the concrete.
The miniature teenager will have feet with areas similar to the ends of small screwdriver blades. Place two of these vertically with the tips touching the soft soil of a typical back yard and try standing on them. They will immediately sink into the ground. Without doing any further analysis, it’s possible to say that Szalinski’s two kids and their two friends are never going to make it across the yard.
There’s only one other conceivable way to shrink children: remove some of their molecules. Removing electrons isn’t helpful because they don’t have enough mass—not to mention that it would create ions and alter chemical bonds. Removing protons alters atoms into completely new materials. Pull a proton out of an oxygen atom and it becomes nitrogen. Doing this to the oxygen atoms in a room would suffocate its occupants. Removing neutrons eventually results in unstable radioactive isotopes. Take a neutron out of normal oxygen and it becomes a radioactive isotope that decays rapidly into an isotope of nitrogen. This process has a half-life of only 122.2 seconds. In other words, half of the radioactive oxygen is gone in a little over two minutes.
Removing an atom from a molecule creates a totally different compound. Taking an oxygen atom from a water molecule converts it to hydrogen gas. So removing atoms also can’t be done. The only possibility left is removing whole molecules.
The question becomes, how many molecules can be removed before problems arise? Sweating, for example, removes molecules, but at some point it results in dehydration. To analyze this possibility, let’s assume that the miniature person has to end up with the same density as he started with. We have to first do a little magic (called algebra) to understand this:
STARTING WITH THE DEFINITION OF DENSITY
Density = mass/volume
We can derive the following:
Mass = (volume) × (density)
This equation says that mass will be directly proportional to volume since density will be constant. For example, if volume is decreased by a factor of 10, mass will decrease by a factor of 10. Obviously, we need to know how volume scales up and down to find out how much the mass has to decrease when shrinking a teenager.
To understand this, imagine a sphere. Its volume is equal to 4/3 pi times the quantity of the radius cubed. In this case, if we scale the radius up by a factor of 10, the volume increases by 103, or 1000. Likewise, if we scale down by a factor of 10, the volume decreases by a factor of 103, or 1000. In other words it will be 1/1000 of its original size. It turns out that regardless of an object’s shape, its volume will scale up and down with the cube of the scaling factor, in other words with (scaling factor)3.
If a teenager is shrunk by a factor of 100, her volume will decrease by a factor of 1003, or 1,000,000. This means for every molecule left in the tiny version of the teenager, 999,999 molecules will have to be removed. We could, perhaps, remove cells instead of molecules, but imagine what would happen to a person if 99.9999 percent of his or her brain cells were removed.
According to the first law of thermodynamics (see Chapter 3), all the removed molecules can’t simply disappear. They have to go someplace, for example, into a barrel of goo. The barrel of goo is certainly a problem, but it’s only the beginning. It’s going to be a nightmare figuring out which molecules in what ratios have to stay in order to end up with a working human after miniaturization. The situation gets worse when considering that humans are warm-blooded.
Like all warm-blooded creatures, humans have to eat a great deal of food just to maintain their body temperature. This food intake is proportional to surface area and scales down by the square of the scaling factor. Hence, the tiny teen’s food requirement will be 1/10,000 times what it was in her full-sized form. So, what’s the big deal?
Assume the normal teen eats 1 percent of her body weight in a day to maintain her temperature. Her food intake has certainly decreased, but her volume has decreased even faster since it scales down by the cube of the scaling factor. Because density was held constant, her mass and weight have decreased by the same factor as her volume. So, she will now have to eat 100 percent of her body weight every day just to maintain her temperature. Even if the ambient temperature is 70 degrees Fahrenheit (21°C), she would have to eat constantly to avoid hypothermia. This is why small critters such as ants are typically cold-blooded. It is also why tiny warm-blooded animals such as shrews have to eat constantly.
Even allowing for some magic, physics says that scaling a human down by large factors simply can’t be done if it’s desirable to keep her alive. Obviously, scaling problems are major flaws in movie physics and should immediately kill the chances of getting anything better than an RP rating. So why is Honey I Shrunk the Kids not even rated? Simple, it’s a Disney family movie. There is not a speck of serious science fiction in it. It’s supposed to be silly, and it is.
SCALING UP HUMANS
In a sequel called Honey I Blew up the Kid [NR] (1992), Rick Moranis is again creating accidental science experiments. This time, his two-year-old son Adam gets blown up to gargantuan size.The youngster is no Godzilla, but he does treat his neighborhood like a giant toy box.
Once again, there are only two conceivable ways to expand a kid. The first is to increase the space between and inside of molecules. This would likely change him into a random cloud of gas or ions that would disperse at the first sign of wind. However, let’s assume that by magic his molecules stay together but with more space between them.
By How Much Could a Human Be Scaled?
To fully answer this question we’d have to define what it is to be human. A very large or very small human would likely not have the same thinking ability (it could be better or worse), lifespan, movement, or biological design as a human on the opposite end of the spectrum.
The shortest recorded man was Gul Mohammed at 1.88 feet (0.572 m) and the tallest Robert Wadlow at 8.93 feet (2.72 m), for roughly a scaling factor of 4.8 between the two.
Allowing a little extra room, it seems likely that the largest humans could be about five times bigger than the smallest ones and still live. In other words, adult human heights could range from about 1.8 feet (0.549 m) to about 9 feet (2.74 m). The large humans would have 1.5 times the difference in blood pressure between their feet and head and likely have more health problems, including early heart failure, than those who are a more normal size of 6 feet (1.8 m) tall. (Wadlow died of an infected foot blister at age 22.) The pressure load on their joints would be 1.5 times higher than the 6-foot person, possibly leading to early arthritis. While their food intake would be less per unit of body weight, such large people would have to eat about 2.3 times as much food and spend more time finding and consuming it than the 6-foot person. Their brains would be larger than normal, but with longer nerves, bigger organs to control, more challenges to their immune systems, higher food requirements, and so forth, they’d likely not be any better at reasoning and problem solving than their normal-sized counterpart.
As for the miniature humans, while they might have some arthritis advantages, their blood vessels would be far smaller than normal and, hence, more prone to clogging. They would have to eat a greater proportion of their body weight in food to maintain their temperature and so would have to spend more time eating. With their much smaller brains they’d certainly have no advantage in thinking ability. Normal-sized humans really are near the optimum size.
In the movie, the youngster is scaled up by roughly a factor of 50. His volume increases by a factor of 125,000. Since his mass remains constant, his density will also decrease by a factor of 125,000. In other words, he will be 1/125,000 times as dense. Humans have a density similar to water (1.0 g/cc) because they are mostly water. Hence, the expanded youngster will end up with a density of 8 × 10-6 grams per cubic centimeter. This is less than 1/10 the density of hydrogen gas, which is about 9 × 10–5 grams per cubic centimeter. In other words, the title of the movie should be Honey I Blew up the Kid and He Blew Away.
&nb
sp; The other alternative is the constant density approach. Add 124,999 molecules to the kid for every one he now contains. He’d have to be pumped up with an Olympic-sized swimming pool full of goo, all the while hoping the molecules would all somehow find their proper place. If we assume the additional molecules wouldn’t kill him, there would be other serious problems.
We can model the youngster’s leg bones as though they are vertical cylinders similar to the columns that held up ancient Greek temples. Of course, this assumes he is standing. In this position, the leg bones or columns’ ability to hold up weight will be proportional to their cross-sectional area—in other words, the area of the circle that would just fit around the outside of the column.
Note that the load on a leg of a standing child, or adult for that matter, is caused by gravity.This acts in the vertical direction and is called a compression load since it tends to compress the leg. The cross-sectional area is in a horizontal plane. In other words, the cross-sectional area that determines the strength of the leg is perpendicular to the compression load’s direction.
Since cross-sectional area is indeed an area, it will scale up and down with the square of the scaling factor. Hence, if the bone’s diameter is doubled, its cross-sectional area and subsequent ability to support weight will increase by a factor of 22,or 4 (assuming no change in material properties). Obviously, its strength will increase or decrease very rapidly when scaled up or down.