Universal Mathematics: All Life on Earth Is Bound by One Spooky Algorithm | Geoffrey West


So I think it’s one of the more remarkable
properties of life actually, but just taking mammals: that the largest mammal, the whale,
is—in terms of measurable quantities of its physiology and its life history—is actually
a scaled up version of the smallest mammal which is actually the shrew, but a mouse is
very close to that. And everything in between, that they are scaled
version of one another and in a systematic predictable way to sort of 80 percent or 90
percent level. So the kinds of things that you might measure
might be as mundane as the length of the aorta, which is the first tube coming out of your
heart, or it could be something as sophisticated and complex as how long each one of these
mammals, for example, is going to live or how long it takes to mature. So all of these things scale in a very predictable
way and they scale in a way that’s nonlinear. So even though it’s simple it’s highly
nonlinear, and that can be expressed in the following way. So perhaps the most well known of these is
the scaling of metabolic rate. And metabolic rate is maybe the most fundamental
quantity of life because metabolic rate simply means how much energy or just how much food
does an animal need to eat each day in order to stay alive. And everybody’s used to that and is familiar
with that. It’s sort of roughly 2,000 food calories
a day for a human being. So you can ask “what is that for different
mammals?” and what you find is that they’re related to one another in a very simple way
despite the fact that metabolism is maybe the most complex physical chemical process
in the universe. It’s phenomenal because metabolism is taking
essentially almost inorganic, something that’s inorganic an making it into life. And so here’s this extraordinary complex
process and yet it scales in a very simple way. And you can express it in English, it can
be expressed quite precisely in a very simple mathematical equation but in English it’s—roughly
speaking—that every time you double the size of an organism from say two grams to
four grams or from 20 grams to 40 grams or 20 kilograms to 40 kilograms or whatever and
just doubling anywhere. Instead of what you might naively expect—double
the size, you double the number of cells roughly speaking; therefore, you would expect to double
the amount of energy, the amount of metabolic energy you need to keep that organism alive
because you have twice as many cells—Quite the contrary you don’t need twice as much. Systematically you only need roughly speaking
75 percent as much. So there’s this kind of systematic 25 percent,
one-quarter “savings.” And it turns out that anything else you measure
as I mentioned a moment ago scales in a similar way with this sort of 25 percent role occurring
in some interesting way. So, for example, if you take mammals: we have
beating hearts, we have a circulatory system with a beating heart. So every time you double the size there’s
a systematic decrease in heartrate as most people are familiar with. An elephant’s heart beats much slower than
ours and ours beats much slower than a dog’s or a mouse’s, for example. And that also obeys this kind of quarter-power
scaling, so in a very systematic way we see this repetitive nature. And what is amazing about that is that each
animal, each one of these animals—and by the way it’s not just true for animals,
it’s also true of plants and trees—but each one of these organisms has evolved by
natural selection, each subsystem has evolved evolutionary by natural selection, each cell
type, each genome that comprises of the organism has its own unique history that ended up being
this particular organism. So you might have expected, in fact, you would
sort of think of that (and often colloquially we think of it) as some kind of random process,
natural selection. And that you would therefore have expected,
if you look at something like metabolic rate or length of aortas or whatever it is, lifespan—They
would sort of be randomly distributed because they would simply represent or reflect the
evolutionary history of that organism, or of the components of that organism. And quite the contrary, as I say, it’s not
that. Somehow natural selection has been constrained
by some underlying principles. And what I have spent quite a lot of time
thinking about and developing a theoretical structure based on underlying principles and
put into a mathematical framework for understanding where that regulatory comes from, and why
it should be this number one-quarter. Where does that magic number fall—so to
speak, arise? And the work that I did with some marvelous
biology colleagues, Jim Brown and Brian Enquist, we developed this what I consider very elegant
theory: that what these scaling laws are reflecting are, in fact, the generic universal mathematical
physical properties of the multiple networks that make an organism viable and allow it
to develop and grow and so on. And the ones we’re all familiar with, many
of them like our circulatory system and our respiratory system. But our neural system is like that, it transmits
information. But these are networks that have evolved to
distribute energy from something macroscopic like a heart or a pool of blood down to deliver
oxygen to the cells by going through a hierarchy called network delivering as I say oxygen,
resources, metabolic energy to the cells. And it is the universal properties, the universal
mathematical properties of those networks that transcend the evolved design. So the same mathematical – now this is extremely
important. It’s the same mathematical and physical
principles applied to a mammal which has a beating heart as applied to a tree. And a mammal, you know, our circulatory system
is a bunch of tubes like in your house the plumbing and the building that we’re sitting
in. That’s our circulatory system. But a tree and a plant, they’re not like
that. They’re a bunch of fiber bundles kind of
joined together like electrical cables that spray out, and that’s what you see when
you see a tree. In each branch there’s actually just these
fibers transmitting, transporting fluid to the leaves and so on. And they don’t have beating hearts as we
well know. And yet they satisfy the same mathematical
principles, and those mathematical principles give rise to this quarter-power scaling in
mammals but also in plants and trees. But also in fish and birds and crustacea (in
principle) and insects and so on. That’s the idea. So one of the nice things about this theory
is that if you like it’s kind of a unified theory because it brings – since metabolism
underlies, you know, pretty much the way we live, the way any organism lives because it
is the way energy and resources are being supplied to cells and so forth.

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