All-Star Superman Biological Review: The Square-Cube Law
This is the second of three posts on the biology in Grant Morrison and Frank Quitely’s All-Star Superman #1.
2. The Square-Cube Law
Dr. Quintum: Normal restrictions on human size and anatomy just don’t apply in weightless conditions.
What Dr. Quintum is referring to here is the Square-Cube Law. This is a fairly straightforward mathematical law which states that when you increase the size of an object by a factor of x, then its surface area will increase in proportion to x2 and the volume will increase in proportion to x3.
This law applies not only to abstract objects, but to living organisms as well. When an organism increases in size, its surface area and volume increase by much larger amounts. This is vital in living creatures as both volume and surface area are important biological factors.
Let’s use Giant Man as an example. Hank Pym, normally 6 foot tall and 200 pounds, decides to grow to 30 feet (for the metricly inclined, normally 1.8 m tall with a weight of 90.7 kg, Pym grows to 9.1 m). Thus he is increasing his size by a factor of 5. His surface area increases by roughly 52 ( or 25). This is key because muscular strength is dependent on area. His volume increases by 53 (i.e. 125). Weight corresponds with volume, so Giant Man now weighs 200 x 125 = 25,000 pounds (11,339.8 kg). The human body, even at 30 feet tall, is not designed to handle that kind of weight. His leg bones would snap like twigs and Giant Man would collapse on the ground in tremendous pain. He probably doesn’t even have enough strength to expand his rib cage to inhale, so he’d suffocate while he lay bleeding on the ground. He doesn’t even have the strength to scream for help (or even to whisper “Avengers Assemble” or “Avengers Disassemble”). Not a pretty picture, eh?
The human body seems to max out at around 8 feet, and even then, most people that tall have significant health problems.
Now I know that everyone is thinking about elephants and other large animals. Remember that these creatures have evolved over hundreds of thousands of years to be able to handle this extra weight. They are quadrapedal and fairly stocky with much stronger and heavier bones. However, even elephants have a maximum size dictated by the Square-Cube Law.
Dr. Quintum suggests that a weightless environment would allow an organism to escape these restrictions. That’s true…to a point. I suspect a weightless environment would allow for creatures to overcome the strength versus weight consequence of the Square-Cube Law. However, while that is the most graphic consequence of the law and the most common example, it is not the only limitation the Square-Cube Law imposes.
Surface area is a vital part of biology. For example, air exchange in the lungs and the absorption of nutrients from the gastrointestinal tract are both dependant on surface area. Increasing the size of an organism would increase its volume and mass to a much greater degree than the surface area of these organs. A creature that much larger than normal would have a difficult time getting enough air and other nutrients to function. Blood flow would be still another concern.
These restrictions could probably be overcome with the judicious use of technology and/or genetic manipulation, and Dr. Quintum seems to have both. Maybe Giant Man should give him a call.
November 30th, 2005 at 1:07 am
The best compliment I can give you is that every time I come away from this blog, I feel a lot smarter.
November 30th, 2005 at 6:33 am
Actually, transfer across membranes (respiration and absorption) wouldn’t depend on the square of the linear measurement in a mammal, because the surfaces involved are highly convoluted. Area would increase in a manner much closer to the cube than the square. Consider the enormous surface area of our own lungs — if we had simple bags for lungs (like a frog) we’d suffocate in minutes.
Also, there have been enormous bipeds, notably the carnosaurs. They did have thicker bones than us humans, of course.
Carl
November 30th, 2005 at 10:40 am
The manga/anime Planetes deals with the idea of the limitations of the human body in a weightless or reduced gravity environment quite well. One of the ’subplot’ stories revolves around a girl who is one of only a handful of people born and raised on the moon. At the age of twelve, she appears to have reached full ‘adult’ size (unlike your average anime 12 year old, usually drawn as appearing much younger) and is constantly being studied by doctors and researchers trying to figure out both her current physiology and potential limits. If I recall, they don’t believe she will ever be allowed to go to Earth, because her bones are not sufficiently developed to be able to stand the stress of full gravity.
November 30th, 2005 at 10:57 am
Official Comment
Carl:
I’ll grant you that there were some giant bipeds in the distant past, but as you point out, they had evolutionary adaptations to support their weight. Plus they had big freakin’ tails.
I will disagree about membrane transfer. Humans (and other mammals [and maybe other classes too]) have developed anatomic strategies to increase the surface area of their organs (such as alveoli in the lungs and villi and microvilli in the intestines)precisely because surface area is so important. Convoluted or not, it still all comes down to surface area; these convoutions exist only to allow the body to maximize surface area. As such, it won’t increase to the same extent that volume will when enlarging the organism and a mis-match will occur.
MsCongeniality:
Similar points are made in Larry Niven’s science fiction books The Smoke Ring and The Integral Trees.
November 30th, 2005 at 11:34 am
Well, there are real-world, Terran, examples of weightlessness’ “escape” from the square-cube law. Aquatic animals often run much larger than terrestrial critters in similar ecological niches, precisely because supporting their own weight is almost a non-issue. Of course, food/energy supplies are still an issue — note that the largest modern animal, the blue whale, is a filter feeder that feeds on krill, way down the food chain and therefore plentiful. As noted above, gas and nutrient exchange are typically handled by structural involution.
Regarding Giant-Man, the Marvel universe implies (though IIRC never explicitly states) a “dualistic” justification for super-strength and the survival of such “enlarged” creatures. Lifeforms in general, and especially humans, are supposed to have a non-corporeal “energy field”, which can tap into “cosmic” (that is, external) energy sources to provide the energy implied by most super-powers. There are also hints of “morphogenetic fields” in their handling of some shape-changers.
November 30th, 2005 at 5:50 pm
Scott, about surface area, note that I didn’t say the area of the lungs would increase as the cube. It would be closer to the cube than to the square, but some of the volume would be wasted on non-respiratory areas for what amounts to tubing. For us that would be the familiar bronchii and bronchioles. If the chest were just packed with alveoli, then area would increase as the cube, as you should be able to see by evaluation (as my old calc teacher used to say).
November 30th, 2005 at 5:51 pm
Actually I meant “by inspection”. Drat.
November 30th, 2005 at 9:40 pm
If you run a man thru an enlarger that just scales him up then the surface area of the lungs and intestines will only increase at x-squared rate versus the x-cubed rate of his mass and most energy needs. But if you grow a person to giant proportions the development program would probably maintain it’s fractal nature resulting in an increase in exchange capacity more proportionate to the increased needs. Of course his skin surface would only increase at the slower rate so he’d be liable to overheat unless changes were made to the lower the basal metabolic rate of heat production or provide enhanced cooling. Of course being entirely anaerobic and using liquid nitrogen for blood indicates what you might quantify as big-ass changes to the metabolism.
Two things about liquid nitrogen:
1) It’s very cold so you’d need a different set of chemical reactions for a lifeform that’s supposed to live at the same pace we do. Our biological rxns are practically stopped entirely at such temperatures, conversely they’d, well explode at ours.
2) It’s non-polar, unlike water or ammonia, so solvation and protein (or whatever) folding rules would be radically different than those our biology is based on two. So on that account kind of a you can’t get there from here aspect to the idea of converting human metabolism into something like that.
December 2nd, 2005 at 12:21 pm
Canonically speaking, the blood-and-air thing has been an issue for Hank Pym, and for the most part the only issue.
On the other hand, ionically-powered and ionically-consisted size changers don’t have the same problem.
So Goliath can and did beat the shite out of Giant Man just because Giant Man’s powers are limited by how much oxygen he can circulate.
Surface area is not an issue nor is mass per se. It’s just that thanks to respitory restrictions he is not capable of doing much in giant form.
January 26th, 2009 at 5:00 am
Great post thanks.
“Similar points are made in Larry Niven’s science fiction books The Smoke Ring and The Integral Trees.”
When I read that I decided to bookmark your page. Niven is one of my all time favorite authors, and you quote two of his lesser known works! Speaking of Niven in regards to Superman, did you read “Man of Steel, Woman of Kleenex”?
Leave a Reply
Contact Me
About
Subscribe:
The Best Of...
Special Topics
Archives
Categories
Twitter
Comic Blogs
Medical Blogs
Currently Reading
Arbitrarily Interesting Medical Condition
Syndrome
The Net:
Contents may have settled during shipping. Past results are no guarantee of future performance. No animals were harmed during the production of this product. Void where prohibited by law. All rights reserved. Not valid with other offers or specials. Professional driver on a closed track. Your financial institution may impose other fees. All models are over 18 years of age. Employees must wash hands before returning to work. Results not typical. Many suitcases look alike. 18% gratuity added to tables of six or more.
Do not taunt Happy Fun Ball.
© 2004-2009 Polite Dissent. Powered by WordPress