"The Strange Laboratory of Dr. LaBarbera," University of Chicago Magazine, October-December 1996

The University of Chicago Magazine

October-December 1996

Continued

One popular motif in monster movies is to take something out of its usual context--make people small or something else (gorillas, grasshoppers, amoebae) large--and then play with the consequences. From a biologist's perspective, Hollywood's approach to the concept has been hopelessly naive.

In The Incredible Shrinking Man (1957), the hero is exposed to radioactive toxic waste and finds himself growing smaller and smaller. Fending off the household cat, he becomes lost to family and friends and must make his own way in a world grown monstrously large, foraging food from crumbs and drinking from puddles of condensation. In one famous scene, he defends himself against a house spider now as tall as he; an abandoned sewing needle becomes his lance, although he has to struggle to lift it.

Stop the projector! Time for a little analysis. Size, in and of itself, affects almost every aspect of an organism's biology. Indeed, the effects of absolute size are so rich in biological insight that the field has earned a name all its own--"scaling."

The conceptual foundations of scaling relationships lie in geometry. Take any object--a sphere, a cube, a humanoid shape. Each has a number of geometric properties, such as its length, area, and volume. All areas will be proportional to some measure of length squared (i.e., length times length), while volumes will be proportional to length cubed (length times length times length).

Now, if you change the size of this object but keep its shape (or relative linear proportions) constant, something curious happens. Let's say that you increase the length by a factor of two. Areas are proportional to length squared, but the new length is twice the old, so the new area is proportional to the square of twice the old length; the new area is not twice the old area, but four times the old area. Similarly, volumes are proportional to length cubed, so the new volume is not twice the old, but two cubed or eight times the old volume. As "size" changes, areas change faster than linear dimensions, and volumes change faster than areas.

What does this mean to the Incredible Shrinking Man--or to any other organism? Related aspects of an organism's biology often depend on different geometric aspects. The rate at which oxygen can be extracted from the air, the rate at which food is digested and absorbed, and the rate at which heat is lost from the body are all proportional to areas (lung, gut, and body-surface areas, respectively). But the rate at which oxygen or food must be supplied and the rate at which heat is produced is proportional to the animal's mass or volume.

Since the geometric bases underlying these functions change at different rates, size change alone implies that such related functions must also change at different rates. If the animal is to remain functional, either functional relations must change or shape must change.

When the Incredible Shrinking Man stops shrinking, he's about an inch tall, so he's down by a factor of about 70 in linear dimensions. Thus, his body's surface area (through which he loses heat) has decreased by a factor of 70x70 or about 5,000, but the mass of his body (which generates the heat) has decreased by 70x70x70 or 350,000 times. He's clearly going to have a hard time maintaining his body temperature (even though his clothes are now conveniently shrinking with him) unless his metabolic rate increases drastically.

Luckily, his lung area has only decreased by 5,000 fold, so he can get the relatively larger supply of oxygen he needs, but he's going to have to supply his body with much more fuel; like a shrew, he'll probably have to eat his own weight daily just to stay alive.

Because of these relatively larger surface areas, he'll be losing water at a proportionally larger rate, so he'll have to drink a lot, too. We see him drink once in the movie--he dips his hand into a puddle and sips from his cupped palm. The image is unremarkable and natural, but unfortunately wrong for his dimensions, a size where surface tension becomes a force comparable to gravity. (The relative importance of various physical forces is also size-dependent because of scaling considerations, a subject too complex to explore here--please take my word for it.) More likely, he'd immerse his hand in the pool and withdraw it coated with a drop of water the size of his head. When he put his lips to the drop, the surface tension would force the drop down his throat whether or not he chooses to swallow.

As for the contest with the spider, the battle is indeed biased, but not the way the movie would have you believe. Certainly the spider has a wicked set of poison fangs and some advantage because it wears its skeleton on the outside, like armor. On the other hand, our hero's increased metabolic rate would have him bouncing around like a mouse on amphetamines. He wouldn't struggle to lift the sewing needle--he'd wield it like a rapier because his relative strength has increased about 70 fold, although he may have problems with balance during his lunges. (The forces that can be produced by a muscle are proportional to its cross-sectional area; the weight of an animal is proportional to its volume.) Pity the poor spider.

Understanding scale is key to problems raised in another classic of life on the small side. Dr. Cyclops (1940) is a tale of a mad scientist who retires to a remote island to perfect his secret machine, a device that emits atomic rays (five years before the bomb!) shrinking anything in their path. When his solitude is disturbed by interlopers (I'm convinced he mistook them for a granting agency's site-inspection team), he shrinks them; the rest of the movie follows the battles between the giant doctor and his miniaturized visitors.

Much of the film is taken up with the Lilliputian team's struggles to get up onto pieces of furniture and then back down again. At least for the latter, they need not have invested so much time and effort in securing pieces of string and thread to use as ropes: They could simply have jumped.

When an object falls, it accelerates until its drag force equals the force generated by gravity acting on its mass; from then on, the velocity is constant. This speed is known as the "terminal velocity"; for a full-sized human it's about 120 mph and is very terminal indeed. However, the drag on an object is proportional to its cross-sectional area, while the force due to gravity is proportional to its mass (and thus volume, if density is constant). As objects get smaller, gravitational pull decreases more rapidly than drag, so terminal velocity decreases.

Of course, as an old gem of black humor notes, it's not the fall that hurts you, it's the sudden stop at the end. A falling object acquires kinetic energy. That energy, proportional to the velocity squared, must be dissipated to bring the object to a halt. Here's where being small is a good thing. Not only do smaller objects fall more slowly, but because of the squared-velocity term in the kinetic energy relationship, there is much less energy to be dissipated on impact and thus less injury.

Indeed, sufficiently small animals cannot be hurt in a fall from any height: A monkey is too big, a squirrel is on the edge, but a mouse is completely safe. The mouse-sized protagonists in Dr. Cyclops could have leapt off the tabletop with a cry of "Geronimo!," secure in the knowledge that they were too small to be hurt.

The epitome of the small-fry genre may be Fantastic Voyage (1966), based on an Isaac Asimov novel almost as bad as the movie. A famous scientist, Vital To The National Defense, has an inoperable blood clot in his brain. Luckily, a secret government project has just developed a machine that can miniaturize objects, and they shrink a submarine and five crew members down to microscopic size and inject them into the comatose scientist's bloodstream to find and destroy the clot. Lacking a copy of Gray's Anatomy, they have more adventures than they should.

Depending on the scene, the scale of the hemonauts varies from viral to bacterial, and there arises a host of problems. First, how do they see? The crew spend time enjoying the scenery as they cruise the arterial byways, but at their largest size, their eyeballs are still much smaller than the wavelength of visible light; even hard ultraviolet radiation is too long in wavelength to be useful. Perhaps they are using X-rays, but if so, their hapless host has more to worry about than a blood clot.

In another scene, Raquel Welch floats in a capillary, controlling the sub remotely with a panel strapped to her waist. Remember that molecules are in constant, vigorous motion, driven by thermal energy. Each second, trillions of molecules collide with your skin; these collisions average out to produce what we macroscopically call pressure. As objects get smaller, this random bombardment still averages out over time, but at any instant more molecules may collide with one side of the object than the other, pushing it momentarily to one side.

This phenomenon, first described by Scottish botanist Robert Brown in 1827, is known as "Brownian motion"; the pollen grains he observed through his microscope appeared to "dance" randomly in the water. Our hemonauts, ten times smaller than Brown's pollen grains, are going to experience the same random and continuous jostling, rather like an endless journey on a train running on bad tracks. Raquel Welch would have been lucky to keep her hands in the vicinity of the control panel, much less actually operate the controls.

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