The Math Formula That Tells Us How Long Everything Will Live

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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.

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.


According to West—and the studies that found this relationship, like this one titled Allometric scaling of plant life history—you can apply this math to any living beings and find their life expectancy with absolute precision. That doesn't mean that it will tell you when one specific giraffe will die, but when all giraffes are supposed to die. Accidents, from a draught to the encounter with a predator to a random DNA mutation, affect the individual. But all giraffes have a set number of days to live, and there's no way around it. In fact, the only animals who have been able to overcome this by means of medical technology are human beings.

It's an extraordinary look at the world, the idea that there's something invisible that governs us all, a mathematical system that clocks biological life at all scales. We know that it is there, says West, but we don't know "where in hell does that number come from":

This can hardly be an accident. If you see scaling, it is manifesting something that transcends history, geography, and therefore the evolved engineered structure of the organism because it applies to me, all mammals, and the trees sitting out there, even though we're completely different designs.

The big question is where in the hell does that number come from? And what is it telling us about the structure of the biology? And what is it telling us about the constraints under which evolution occurred? That was the beginning of all this.


Above: the study that predicted the life of plants.

See, West is proposing that the same constants that regulate life also regulate how other complex systems growth. There is a law, he proposes, that connects it all in a very simple—although mathematically extremely complex way—common way.

The second thing is, (again, comes from the data and the conceptual framework explains it) the bigger you are, the slower everything is. The bigger you are, you live longer. Oxygen diffuses slower across your various membranes. You take longer to mature, you grow slower, but all in a systematic, mathematizable, predictable way. The pace of life systematically slows down following these quarter power scales. And again, we'll ask those questions about life ... social life and economies.

The work I got involved in was to try to understand these scaling laws. And to make it a very short story, what was proposed apart from the thinking was, look, this is universal. It cuts across the design of organisms. Whether you are insects, fish, mammals or birds, you get the same scaling laws. It is independent of design. Therefore, it must be something that is about the structure of the way things are distributed.

You recognize what the problem is. You have ten cells. You have this problem. You've got to sustain them, roughly speaking, democratically and efficiently. And however natural selection solved it, it solved it by evolving hierarchical networks.


To me, this convergence of sciences, this singular rule to rule them all, is perhaps the most fascinating quest in the history of humankind. One that, I hope, will be revealed before I die, even before they discover the warp drive.


Maybe Douglas Adams was right all along and the answer is 42.

Watch West's interview here.
Image by Yunfan Tan