Category Archives: science

There’s a Math Formula That Tells Us How Long Everything Will Live


NPR’s Robert Krulwich has a whimsical piece on the one formula that rules it all, from unicellular organisms to whales and sequoias and humans. A math formula that governs our life and tells us when to die.

Even more interesting: the same system scales to other things too, like societies and economies. And it’s all bound by one seemingly magic number.

live and die : ehack

live and die : ehack

Physicist Geoffrey West describes it a very must-watch with Edge:

[…] if you plotted, for example the metabolic rate on the Y axis and size on the X axis, because of the extraordinary diversity and complexity of the system and the historical contingency, you would expect points all over the map representing, of course, history and geography and so on.

Well, you find quite the contrary. You find a very simple curve, and that curve has a very simple mathematical formula. It comes out to be a very simple power law. In fact, the power law not only is simple in itself mathematically, but here it has an exponent that is extraordinarily simple. The exponent was very close to the number three quarters.

First of all, that was amazing in itself, that you see scaling. But more importantly was that the scaling is manifested across all of life into eco-systems and down within cells. So this scaling law is truly remarkable. It goes from intracellular up to ecosystems almost 30 orders of magnitude. They’re the same phenomenon.

Furthermore, if you look at any physiological variable, such as the rate at which oxygen diffuses across lungs, the length of the aorta, anything to do with the physiology of any organism, or if you look at any life history event like how long you live, how long does the organism live, how long does it take to mature, what is its growth rate, etc., and you ask how does it scale? It scales in very similar way.

That is, it scales as a simple power law. The extraordinary thing about it is that the power law has an exponent, which is always a simple multiple of one quarter. What you determine just from the data is that there’s this extraordinary simple number, four, which seems to dominate all biology and across all taxonomic groups from the microscopic to the macroscopic.

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