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By Chris Whittaker April 28, 2008

Size Matters!

In the classic science fiction movie Them! from the 1950’s, giant radioactive ants push mankind to the doorstep of extinction. It’s a theme that Hollywood loves. Giant super-strong and virtually indestructible creatures take over the world. One look at ants – the real ones – makes it easy to see why our imaginations are so easily fired up.

Ants are incredible creatures. They are industrious, incredibly strong and almost indestructible. To see this, all you have to do is get down on your knees on a patch of grass and watch an ant move an object many times its size. In fact, ants can carry up to fifty times their own weight! That’s like you or I being able to pick up minivan or two. What’s more, if you drop an ant out of a ten storey window, not only does it survive but it barely seems to notice when it hits the ground! So if tiny ants are like this, then giant ants would surely be the end of us. At least that’s what the producers of B-movies like Them! want us to think. But fortunately, reality has little to do with the silver screen. It turns out that giant ants would be anything but scary. The worst they could do is die, rot and make a stench. You see, giant ants would not be strong, nor would they be indestructible. In fact, they couldn’t even breathe or lift themselves off the ground let alone fly to Los Angeles and infest the sewers as they eventually do in Them!. You name them, King Kong, Godzilla, Mothra, the 50 foot woman, even the Stay-Puff marshmallow man from Ghostbuster’s (tragically) couldn’t do much of anything to terrorize anyone. Why, even the mighty tyrannosaurus rex – real ones from the past, not from Jurassic Park - could have been outrun by any reasonable adult on foot and a t-rex surely would have died had it tripped and fell. And it all has to do with size.

Size matters in almost every field of science - from biology to engineering, physics to nanotechnology – but it goes beyond that. Size matters in how we make sense of the world and our place in it. Literature and mythology are full of stories that are meant to help us understand who we are and what our place is in the pecking order of the universe. From Milton’s Paradise Lost to Lewis Carroll’s Alice in Wonderland size is used as a narrative tool to help us see and understand differently. Size also effects how we behave and how we organize ourselves. That much is obvious when faced with a mob or when looking at the way people organize themselves into clans, states, unions or whatever.

Size matters because it is a bridge that helps us understand, it determines what is possible and it shapes our world in amazing ways and yet we seldom seem to pay much attention to it.

In this ongoing blog, I will look at how size matters. Each article will examine size from a different perspective and in a different domain: biology, nanotechnology, history, literature – you name it and I’ll touch on it – except sex (sorry).

My fascination with size started in university when I attended a lecture in geology as an undergraduate student in engineering at Queen’s University. I remember it quite vividly actually. The lecture was in a large and darkly lit auditorium in Ellis Hall and it was being delivered by Dr. “Hockey-stick” Hanes - a teacher we all liked and who used a hockey stick as his pointer for the giant screen at the front of the hall. On this particular day, I don’t remember being particularly interested in what was being said until the topic suddenly turned to ants. I had always assumed that ants were strong for their size because they were different. I expected that they had different kinds of muscles or something. I was not ready to hear that ants were relatively strong simply because they were small. You see, the strength of a muscle – or for anything in general, like a piece of rope or a column of concrete – depends on its cross-sectional area.

For ease of understanding, let’s consider several segments of rope made of the same material but with differing dimensions. Any two pieces with the same thickness will be the same strength. The length of the strings won’t matter (unless we take a thin string and loop it – then it is stronger but only because the act of looping it doubled it’s cross-sectional area). The weight of an object however, depends on volume. Considering our strings again, the thickness and the length matter when it comes to weight. A string that is twice the length is twice the weight but not twice the strength – and herein lies the key to understanding the relative strength of ants. As the size of something – like living things – gets smaller, their weight (volume) decreases faster than their strength (area).

Consider two ropes, one of which is half the size of the other – that is, it’s half the length and half the thickness of the other. The scaled down rope will have a strength that is 2x2=4 times less than the larger one because it has a cross sectional area that is 4 times smaller (remember, area is related to the square of the thickness). But it will have a weight that is 2x2x2=8 times less because the weight depends on the area (thickness squared) and the length. Thus the smaller rope is 4 times weaker but 8 times less heavy. It is therefore twice as strong relative to its weight! Indeed, in general, an object that is 10 times smaller is 10 times stronger relative to its weight. Similarly, an object that is 100 times smaller is 10,000 stronger relative to its weight. Smaller doesn’t mean stronger in an absolute sense but it does mean stronger relative to its weight.

That means that if I can lift my own weight (strength to weight ratio = 1) and I were to be shrunk down to the size of an ant, say 100 times, I would be able to lift 10,000 times my weight. Indeed, I would be a terror to the ants! And if ants were to be enlarged to my size, they wouldn’t even be able to lift themselves off the ground!

In the second blog, I will continue to look at size and scaling in living things, including how size matters when it comes to flying, limits on the size of warm blooded animals, posture and running speeds. At the centre of it all will be this ratio of area to volume and I will suggest – as biologists did for centuries – that this ratio is fundamental to living things. It will turn out however, that nature has a secret up her sleeve and it’s more complicated than that – but that will have to wait for the third blog! I hope you keep reading!

Acknowledgements

Credits for the image go to the movie "Them!" by director Gordon Douglas in 1950. 

Comments

  1. space-default-avatar

    Ray Bourgeois

    March 2, 2009

    Interesting! There’s a lot to explore on this subject.  Ultimately, physics and physiology determine what is possible.  It would be interesting to note that the power of the human jaw maximizes the intersection of the two in humans, and delivers a force of bite around 200lbs.  We can speculate that if humans needed the strength to lift a minivan, we would have been designed differently—but your essay speaks to “can we be designed differently” given the laws of physics/physiology.  There’s room for improvement, I know, for example, even the force of bite is greatly enhanced in some of our simian cousins with the addition of skull crests for the muscles.  But the real limitions is what makes this topic so interesting.

    I hope you get a chance to speak to the merits of endoskeleton versus exoskeleton with regard to your growing ant.  I suspect the exoskeleton design runs into limitations relatively quickly when it comes to force (as opposed to mobility).

    Cheers,
    Ray

  1. space-default-avatar

    Chris Whittaker

    April 20, 2009

    Hi Ray,
    Thanks for the post. You are right that size is more than a minor constraint on the design of living things, it is centrally important. Indeed it may be the single biggest (pardon the pun) factor. There is some incrediblly interesting work on Allometric Scaling by Geoff West and Jim Brown that they claim may be the biology-equivalent of Newton’s Laws in physics. They have developed a theory that successfully predicts quarter-power scaling in biology (something that no other theory had been able to do in the 120 years that we’ve had good data for) which has its origins in the strength versus weight issues noted in the article. But what is even more surprising about Brown and West’s work is that it goes on to describe things like root structures in trees and vegitation and it even predicts the lifespan of living things based on size! Maybe I’ll just have to write another article about it!
    Chris

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