“This one makes you bigger, this one makes you small.” - The Physics of ALICE IN WONDERLAND
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Mar 19 2010, 7:03 PM
By now you’ve probably seen the new ALICE IN WONDERLAND. It’s made over $230 million so far, so if you haven’t see it, apparently you live in an ice cave in Siberia. Or maybe just Pomona.
It’s a Tim Burton fantasy film, so talking about its physics is like talking about the alcohol content of a virgin scotch on the rocks, but it can still be fun to look at the effects of fantasy situations in our Newtonian world. Ever since Larry Niven mused on what would happen if Superman and Lois Lane played hide the solar-powered supersalami in “Man of Steel, Woman of Kleenex” I’ve liked this kind of thing.
One of the central devices of the movie is Alice’s variable size. I don’t know about you, but I can empathize – when I drink certain kinds of liquids I feel 12 feet tall and invulnerable, at least until the bouncer proves me wrong.
When Alice drinks the magic potion she can double or even quadruple in size. It’s like Pfizer’s most famous pharmacological product, but for your whole body.
The trouble is, if our friends at Pfizer managed to invent a little purple pill that made people double in size, they’d quickly find themselves subject to a lot of negligent homicide lawsuits because of all the broken bones, cardiac arrests, and collapsed lungs.
You see, whenever an object increases in size linearly, its mass increases exponentially. Which creates problems for your garden-variety magical size-changing potions.
To get the scoop on this, I talked with Dr. Kevin Grazier of JPL, a physicist who also happens to be the science advisor for Eureka and the various modern incarnations of Battlestar Galactica. He said:
“There are really only two conceivable ways: the person’s mass could increase or decrease according to size, or the distance between their atoms could vary.”
Let’s take these in order. For the first case, the mass differential equation is
26.326 * e^(0.22985 * height)
So, when Alice drinks enough of the potion to tower over the shrubbery in the Red Queen’s garden, let’s say she quadrupled from her “normal” size. If her normal size was 5 and a half feet tall (66 inches) and 120 pounds, we might intuitively assume that she would become 22 feet tall and 480 pounds. But if Wonderland operated according to Newtonian physics, she would actually be over 7,000 pounds.
And the humanoid body simply isn’t designed to bear that kind of load. So the Red Queen wouldn’t say “Off with her head!” but rather something more like “Eew. Someone clean up that 7,000 pounds of collapsed flesh in my garden before it really starts to smell.”
They’d have to call those people who dismember and cart away beached whales. One would only hope that they didn’t use explosives.
(This is to say nothing of the magical properties of Alice’s dress, which seems to have been made by an ancestor to Bruce Banner’s tailor.)
Alice also had a magical cake which makes her smaller. I bet Jenny Craig would kill for that recipe. But similar concerns apply. If Itsy Bitsy Alice might shrink to a few inches tall, but her mass would become untenable to keep her alive.
And when the Mad Hatter put her on his chapeau and flung her across that pond, the centrifugal force would have ripped her itsy bitsy arms out of their sockets. RIP Li’l Alice.
But what if Alice’s change in size didn’t affect her mass? We could do this simply by changing the distance between the atoms of which she is made.
Again, here’s Dr. Grazier:
“At the atomic level, the distance between atoms in a substance at room temperature is quite vast. If we squeezed Alice’s atoms together to shrink her to, say, 6 inches tall, she’s still weigh 120 lbs! If Alice’s atoms were separated even more widely, and again so that she grew to 10 feet tall, and again her mass kept constant, she’d nearly blow away in the slightest breeze.”
Bye bye, Alice.
Luckily, Wonderland operates in a non-Newtonian world, or else it would have looked like a brightly colored sequel to SAW.
By now you’ve probably seen the new ALICE IN WONDERLAND. It’s made over $230 million so far, so if you haven’t see it, apparently you live in an ice cave in Siberia. Or maybe just Pomona.It’s a Tim Burton fantasy film, so talking about its physics is like talking about the alcohol content of a virgin scotch on the rocks, but it can still be fun to look at the effects of fantasy situations in our Newtonian world. Ever since Larry Niven mused on what would happen if Superman and Lois Lane played hide the solar-powered supersalami in “Man of Steel, Woman of Kleenex” I’ve liked this kind of thing.
One of the central devices of the movie is Alice’s variable size. I don’t know about you, but I can empathize – when I drink certain kinds of liquids I feel 12 feet tall and invulnerable, at least until the bouncer proves me wrong.
When Alice drinks the magic potion she can double or even quadruple in size. It’s like Pfizer’s most famous pharmacological product, but for your whole body.
The trouble is, if our friends at Pfizer managed to invent a little purple pill that made people double in size, they’d quickly find themselves subject to a lot of negligent homicide lawsuits because of all the broken bones, cardiac arrests, and collapsed lungs.
You see, whenever an object increases in size linearly, its mass increases exponentially. Which creates problems for your garden-variety magical size-changing potions.
To get the scoop on this, I talked with Dr. Kevin Grazier of JPL, a physicist who also happens to be the science advisor for Eureka and the various modern incarnations of Battlestar Galactica. He said:
“There are really only two conceivable ways: the person’s mass could increase or decrease according to size, or the distance between their atoms could vary.”
Let’s take these in order. For the first case, the mass differential equation is
26.326 * e^(0.22985 * height)
So, when Alice drinks enough of the potion to tower over the shrubbery in the Red Queen’s garden, let’s say she quadrupled from her “normal” size. If her normal size was 5 and a half feet tall (66 inches) and 120 pounds, we might intuitively assume that she would become 22 feet tall and 480 pounds. But if Wonderland operated according to Newtonian physics, she would actually be over 7,000 pounds.
And the humanoid body simply isn’t designed to bear that kind of load. So the Red Queen wouldn’t say “Off with her head!” but rather something more like “Eew. Someone clean up that 7,000 pounds of collapsed flesh in my garden before it really starts to smell.”
They’d have to call those people who dismember and cart away beached whales. One would only hope that they didn’t use explosives.
(This is to say nothing of the magical properties of Alice’s dress, which seems to have been made by an ancestor to Bruce Banner’s tailor.)
Alice also had a magical cake which makes her smaller. I bet Jenny Craig would kill for that recipe. But similar concerns apply. If Itsy Bitsy Alice might shrink to a few inches tall, but her mass would become untenable to keep her alive.
And when the Mad Hatter put her on his chapeau and flung her across that pond, the centrifugal force would have ripped her itsy bitsy arms out of their sockets. RIP Li’l Alice.
But what if Alice’s change in size didn’t affect her mass? We could do this simply by changing the distance between the atoms of which she is made.
Again, here’s Dr. Grazier:
“At the atomic level, the distance between atoms in a substance at room temperature is quite vast. If we squeezed Alice’s atoms together to shrink her to, say, 6 inches tall, she’s still weigh 120 lbs! If Alice’s atoms were separated even more widely, and again so that she grew to 10 feet tall, and again her mass kept constant, she’d nearly blow away in the slightest breeze.”
Bye bye, Alice.
Luckily, Wonderland operates in a non-Newtonian world, or else it would have looked like a brightly colored sequel to SAW.
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