Tuesday 3 January 2006

Pic of the day: Once you think about it, there is really no part of a toddler that is far from its surface.

Square/cube children

No, I'm not talking about the Gamecube. I don't even have a TV. Actually I don't have a child either, but I've seen plenty of those. What I'm talking about is the square/cube law, which is a law of nature rather than of legislation. It explains why a mouse and an elephant have roughly the same number of heartbeats in their lives, even though the elephant lives nearly as long as a human while the mouse lives mere months.

In general, small warm-blooded animals must have a fast metabolism, and large warm-blooded animals must have a slow one. This is because when you double the length of an animal (if all other parts remain in proportion) it gets four times as large surface, but eight times as large volume / mass / weight. Likewise if you triple its size, the surface will increase ninefold, but its mass 27 times! I could prove this mathematically, but then we would have to assume a spherical animal of uniform density, and you really don't want to do that... The short of it is, the small animal has much larger surface relative to body mass, so loses heat fast. To keep it up, it needs to burn calories at a furious rate. The net effect is that they simply live faster.

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Children are not exactly what you'd call animals (well, not out loud in front of the guests) but they grudgingly obey the same laws of nature. Compared to adults, they are more susceptible to cold (and heat). Their hearts beat faster, they need more food compared to their size, and they move faster compared to their size. (Try running around with a preschooler for a while if your heart allows it. The very existence of fat parents is a testament to human ingenuity, and rarely seen in the wild.) Small children fall ill very fast, but they also heal much faster, all other things being equal.

Not only the heart goes faster in the small ones, but also the brain. Consider that a child is born with at most a vague outline of what parts a language ought to contain (and even that instinctive knowledge is contested by some respected scientists). Simply from observing those around it, the child will pick up any language over the course of a few years. If there are several languages in use around it, the child will learn them all at the same time with little delay in any of them. This includes sign language. If an adult were to pick up new languages at the same speed (and few do), that would be with an existing knowledge of what a language is, what it is good for, and largely what parts it contains. The child only knows that people make sounds (or wave their arms) and things happen, and on that basis they absorb the whole thing. At the same time they also get around to learning other basic life skills like eating with a fork, begging from grandparents, washing hands after going to the bathroom, and not picking fights with bigger boys. All at the same time.

In addition to these objective facts, we have the subjective reports of thousands of adults who claim that time is passing much faster than it did when they were children. As clocks and calendars prove beyond reasonable doubt that the days still have 24 hours and the years still at least 365 days, the explanation must be that adults live more slowly. Which is exactly what the square/cube law would lead us to expect.

Now you may want to try to extend your lifespan further by growing even larger through the eager assistance of your friendly local fast food outlet. Alas, this is not how it works. The species is made (or evolved, as most scientists may say) to operate within certain boundaries. Variation within this is not likely to make much difference, at least not compared with the other differences that kick in as you approach the limits of your body. For instance you would think that losing weight would make you live faster, and this may indeed be marginally true at the beginning. But when the body suspects that it is experiencing a famine, it will react by actually lowering the temperature and slowing down some of its processes. Likewise if you put on lots of weight, just moving that weight across the living room will be enough hard work to make your heart beat faster, thus negating any energy-saving effect of your greater mass to surface ratio.

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In conclusion, then, an hour really is much longer to a child than to an adult. It is not just that they are fussing to make you upset. And there is nothing we can do about it, except marvel at the laws of nature at work once again.