Mathematics of Metabolism and Life Expectancy

Size does matter. It matters especially when it comes to the question of life expectancy of various species.This was the profound finding of the Swiss scientist Max Kleiber way back in early1930s. His initial research was focused on cattle. He measured the impact of size on their metabolic rate. Measurement of metabolic rate had good practical value for the cattle industry because it allowed the prediction of food needed for the livestock,which in turn enabled farmers to predict the amount of meat that could be produced after their slaughter. Kleiber found a mathematical correlation between size and metabolic rate of various species of cattle and this encouraged him to study a diverse variety of creatures including humans. Although scientists intuitively knew for a long time that as life gets bigger it slows down , Kleiber was the first scientist to find a mathematical relationship. For instance,flies lived for hours or days while elephants lasted for over half centuries. Basically scientists realized that smaller creatures pumped blood faster than the bigger ones.

Kleiber found that size and life expectancy followed a mathematical relationship which is technically known as ‘negative quarter power scaling’. What does it mean in actual terms? It is better illustrated with an example. Let us,for instance, compare a cow & a woodchuck. A cow is roughly 1000 times heavier than a woodchuck. Applying the mathematical relationship,the square root of 1000 is 31 and the square root of 31 is 5.5. The ‘negative quarter power scaling’ when applied to these two creatures implies that on an average a cow will live 5.5 times longer than a woodchuck and will have a heartbeat rate which is 5.5 times slower than the latter. Indeed this estimate of comparative life span is found to be correct. In fact Kleiber’s Law could be applied to all kinds of species – rats,rodents,pigeons,dogs,even bacteria and plants.
George Johnson , a well known science writer of recent times wrote in one of his books that a nice consequence of the so called KLEIBER’s law is that the number of heart beats per life time tends to be stable(constant) from species to species. Bigger animals just take longer to use up their quota.

As I reflected on the Kleiber’s law,it dawned on me that it has another profound significance for us humans. Let us assume that each one of us is programmed to last for ‘X’ number of heart beats during our life span. Then it pays to use up that quota rather slowly. How can one do it? Simple. Our ancestors in India have taught us a great technique – YOGA & MEDITATION. It is proven scientifically that during meditation our metabolic rate and heart rate slow down tremendously. And consequently,this will contribute towards longer life span. In fact that is what our ancient ‘rishis’ had practiced through penance and austerities which enabled them to live for hundreds and thousands of years!

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Published in: on April 17, 2011 at 8:56 am  Leave a Comment  
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