---
title: 'Why Does Every Mammal Get 1 Billion Heartbeats in Their Life?'
source: 'https://youtube.com/watch?v=tL9Lw250spc'
video_id: 'tL9Lw250spc'
date: 2026-07-26
duration_sec: 2132
---

# Why Does Every Mammal Get 1 Billion Heartbeats in Their Life?

> Source: [Why Does Every Mammal Get 1 Billion Heartbeats in Their Life?](https://youtube.com/watch?v=tL9Lw250spc)

## Summary

The video explores the fascinating phenomenon that nearly every mammal gets about a billion heartbeats in its lifetime, starting with the tragic story of Tusko the elephant, who died from an LSD overdose due to faulty scaling assumptions. It then delves into biological scaling laws, from Kleiber's Law to the WBE theory of fractal networks, and extends these ideas to human longevity and city growth.

### Key Points

- **The Tusko Experiment** [00:45] — Researchers gave an elephant 300 mg of LSD based on linear scaling from cats, assuming safe dose scaled with mass. The elephant died within minutes from seizures.
- **Kleiber's Law** [08:04] — Metabolic rate scales as mass to the 3/4 power, not 2/3 as predicted by surface area. This means larger animals are more energy-efficient per unit mass.
- **WBE Theory** [18:30] — West, Brown, and Enquist proposed that fractal-like networks (e.g., circulatory system) explain the 3/4 scaling. Key premises: space-filling networks, invariant terminal units, and natural selection for efficiency.
- **Heart Rate and Lifespan Scaling** [20:36] — Heart rate scales as mass^-1/4, lifespan as mass^1/4. The product (heart rate × lifespan) is constant at ~1 billion heartbeats for most mammals.
- **Human Exception** [23:18] — Humans live over 2 billion heartbeats due to modern medicine and sanitation, which have extended lifespan beyond the natural scaling prediction.
- **City Scaling** [25:25] — Cities show superlinear scaling for socioeconomic factors (crime, patents, wages) with exponent ~1.15, and sublinear scaling for infrastructure (roads, gas stations) with exponent ~0.8.

### Conclusion

Scaling laws reveal deep patterns in biology and society, but the debate over the exact exponent and theory continues. Understanding these relationships could optimize energy use, urban planning, and even extend human lifespan.

## Transcript

(mellow music) Well, to a reasonable person, But what if you needed to do it for a scientific experiment? a top secret project known as MKUltra,
how drugs like LSD could be used to change human behavior. because elephants are normally quite docile, And the hypothesis was
by the release of an LSD-like substance So if that's true, then administering LSD So the real question was how much LSD should you give
to cause a psychological reaction, Well, the researchers didn't know, LSD had never been given but they did know that the safe dose in cats
Now, since an elephant has around they figured we'll give it a thousand times the dose. an Indian elephant at the Lincoln Park Zoo in Oklahoma.
with nearly 300 milligrams of LSD. But within five minutes, Tusko trumpeted, collapsed, and went into status epilepticus.
but Tusko died shortly thereafter. that safe drug dosage scales linearly with mass.
And it turns out there are a lot of things like this For example, take the smallest mammal by mass, and the largest land mammal, the African bush elephant.
over the course of its entire life? around a billion heartbeats in its lifetime, heartbeats in its lifetime.
A two-toed sloth? what environment they live in, how large they are, they all get around a billion heartbeats
Why not a million? - That is every mammal except one. Scale by Geoffrey West.
What's even more curious is that you can predict a staggering number and reproductive output to its total lifespan.
If you know the population and location, and patent filings to crime rates, disease prevalence, and even the literal speed at which pedestrians walk.
of Tusko the Elephant. is proportional to mass. But it turns out that the speed at which an animal
doesn't depend directly on its mass. That is the number of calories it uses Your heart is pumping, that takes energy.
Digestion takes energy. Everything that you do requires energy. they require roughly 250 kilocalories of energy,
But there is nothing special about a cat's cells. you'll find they're a similar size, similar makeup,
The same is true for other animals. of animals are always roughly the same. has about a thousand times as many cells.
times as much energy. So 250,000 kilocalories per day. - So what's the issue here?
that energy is radiated out in the form of body heat. through our skin, to the environment.
and do the standard physicist thing. Let's assume our animals are perfect spheres. but it does make everything a lot easier to follow.
our 3000 kilogram elephant has a volume a thousand times So its radius must be 10 times larger. That's because volume is proportional to radius cubed.
So the elephant's surface area Generating a thousand times as much heat to radiate it away would end very
If this were the case, it would boil alive. French scientists proposed a different scaling law. and that heat is radiated through the surface,
to the surface area, A, instead. Now, we can rewrite this to see Surface area is proportional to radius squared,
and if mass is proportional to radius cubed, Plugging that in for R, - Really familiar example would
Maybe you want to make a big turkey for Thanksgiving. But that you realize is linear thinking. or the roast, because the heat is coming in
and it's got to do thermal diffusion into the meat. like the characteristic length, It'll go like the dimension squared,
whereas volume of the meat is going to be like length cubed, So when you put those things together, to cook the roast will go like its mass
- So if I'm thinking about cooking a roast Is that two to the two-thirds the time? then you only have to cook it about 60% longer,
- [Host] Similarly, according to this scaling, should only burn a hundred times as many calories. And the appropriate dose of LSD for Tusko
These two wildly different predictions come from different scales as a function of mass. to mass raised to some power.
and all power laws have a special property. you get a straight line. to the exponent of the power law.
If the slope is one, that's just everyday linear scaling. that is called sublinear scaling. that is known as superlinear scaling.
that the two-thirds exponent But then in 1932, Swiss biologist, Max Kleiber,
of different animals from a small dove at 150 grams to a large steer at 680,000 grams, And as expected, all the data did fall on a straight line.
Instead, it was about three quarters. It implies that if you double an animal's mass, an increase of 68% instead of the 59%,
So according to Kleiber's Law, as many calories as a cat, or about 45,000 kilocalories. was 53 milligrams, which is around a sixth of the dose
So that explains the dosing catastrophe Kleiber's original work was based on a small data set, But if you plot the data for a larger range of mammals,
you find that they all follow Now, they don't all fit perfectly onto the same line than for cold-blooded ones,
mass raised to the three-quarters. to single cells and the molecular machines inside of them. spanning more than 25 orders of magnitude.
if an elephant has so many more cells to a cell in a smaller creature, and yet it's using proportionately less energy,
or per kilo or per cell, are functioning with much less energy. and it's hard to understand why.
What is it that the cells are providing to each other, - I just put in my calculator 100 to the three quarters, then according to this, only 31.6
So it seems like a big savings. It's a biological fact, but people have been arguing now for a century
- In the decades following Kleiber's observation, Researchers discovered that brain size also roughly scales and the amount of blood pumped per minute.
- If you ask how long a creature will live, a mammal, to the one quarter power. - [Host] So that means if you double the mass of a mammal,
then on average, its lifespan is around 19% longer. as roughly mass to the one quarter, while breathing rate They're not all three quarters power laws,
So the question on everyone's mind was - One popular theory emerged in the 1990s.
- Most of the biology classes then that you take, and then you have to memorize all the different parts - [Henry] But then one day he took a zoology class
- [Brian] I just couldn't believe it. You know, this is kind of like something fundamental And there I knew immediately that I wanted
kind of plant physiology research - [Henry] So Enquist started studying for his PhD, who had been thinking about scaling laws for years.
there's some form of self-similarity So they wondered, what could that self-similarity be? with the way resources are transported through the body,
They had the biological intuition, they needed a formal mathematical framework. - And at the time, Jim was associated
and he started asking around with, biological scaling relationships? I know of this physicist who's up at Los Alamos
And so we met Geoffrey and it was like immediately, for like years. someone who's been like speaking your language,
to try and find a compelling explanation for Kleiber's Law. - They started by assuming three simple premises. that distribute resources are space-filling,
The second premise is that the terminal units on the outer periphery of the delivery system, That is the outermost blood vessels that carry nutrients
as the ones in a mouse. And the third premise is that over time, toward an efficient design.
Well, intuitively, to get fuel from one place to another So basically a straight line. you would also need many different paths.
the networks inside need to One way to do this is to stretch all the paths In this case, the volume of the animal
Or if we rearrange that, internal path length should scale just like the overall length of the animal does. Take these two regions.
go through almost the same path in the body, before they reach their destinations. and split it only when the paths needed to diverge,
and a lot less blood to fill the vessels. and you end up with a much more efficient design But now we run into another issue
for some of the blood to bounce back, that is reflect. energy to pump blood around. that minimize reflections.
if the cross-sectional area of the vessels So if you've got a cross-sectional area then each of the two branches need to have an area
of one centimeter squared each, for large vessels at least. to allow blood to slow down If you keep repeating this pattern across the network,
you end up with this, a branching self-similar fractal. of the circulatory system, it has this geometry. - But how do you get from this
Well, mathematician Felix Hausdorff discovered (mellow music) Take a straight line segment. Hausdorff assigned this line segment a value of 1.0.
and more bends to those bends. and more fractal-like. that one-dimensional line segment fills up
Hausdorff assigned these space-filling fractal curves The same ideas apply to a 2D surface. Two-dimensional.
that sheet of paper, and it effectively fills So you can now describe that sheet of paper as a sphere instead of a two-dimensional sheet of paper.
at smaller and smaller scales, and a 2D surface In the mathematical limit, it becomes space filling - [Brian] You know, biologically, I said,
That enables an organism for a given size to pack in more of these metabolic surface areas And it's because of this fractal-like structure
and convolutions and on top of each other - As a result, the Hausdorff dimension of the surface
meaning its surface area doesn't scale And since the metabolic rate hinges on well, it must also scale like length cubed.
wanted to explain Kleiber's Law. So they needed to know how metabolic rate scales with mass. around the network should be proportional
And since volume is just surface area times length that means both volume and mass which can be rewritten to show that length is proportional
And if you plug that into the equation must be proportional to mass to the three-quarters, West, Brown and Enquist published their work in 1997,
as WBE Theory, after their initials. It makes very specific predictions. This is sticking your neck out,
(mellow music) - [Derek] Take a look at this table These are the scaling exponents WBE theory predicts, but all follow from the same theory.
should scale with its mass to the three-eighths or .375. to the 11-12ths or about 0.92.
Now, these are the observed data. Lung area, 0.95. They had a table with something like, I don't know,
20 or 30 predictions of exotic exponents, for the three-quarters power of metabolism, that biologists have measured.
once you've got the three-quarters law for metabolism. Heart rate is equal to the blood flow rate The volume of blood per beat has been found
And the blood flow rate? how nutrients get distributed around the body. proportional to one another.
Swapping in the scaling law Kleiber had found, meaning bigger animals should have slower And this is exactly what we observe in nature.
has an extraordinary heart rate of 1200 beats per minute. Whereas the biggest land mammal, the African bush elephant, And we can do something similar for lifespan.
the accumulation of metabolic damage. processes nutrients over time, and that over time causes the animal to die.
is its metabolic rate per unit of mass, If damage accumulates faster, it dies sooner. So lifespan is proportional to M over B,
or substituting in Kleiber's Law, M to the one quarter. And you do see this in nature. while a mighty African elephant can live up to 70 years.
but you live a relatively short life. your heart beats much slower and you live a lot longer. - So it's the, you know, live fast and burnout
Or spend it frugally and live a really long life. Heart rate scales as B over M. And lifespan scales as M over B.
They scale in equal and opposite directions. is just the heart rate multiplied by the lifespan. leaving you with just a constant.
what mammal you're talking about, You can find that number by just plugging in some examples. The shrew's 1200 beats per minute multiplied by a lifespan
around 950 million heartbeats Meanwhile, an African elephant's 30 beats per minute gives you a little over a billion heartbeats.
you keep landing at the same figure of This is why nearly every mammal from a tiny field mouse to a gazelle, from a cheetah to a hippopotamus,
between the day they're born and the day they die. that gets significantly more than a billion heartbeats.
We are the lucky ones. to the standard value of one billion heartbeats. and better sanitation methods became widespread,
and deaths from disease. And with it, the average number of heartbeats in a lifetime. If you look closely, you can also see some significant drops
or over here, what appears to be But overall, the trend is clear. of heartbeats we get in our lifetime to the point
heartbeats before they die. and technology than this. more than a full extra life.
to have much longer lives in captivity when they're away from the hazards they would naturally encounter in the wild. we now have the lifespan of a much larger mammal,
somewhere between an elephant and a whale. (mellow music) Take a look at this graph. In fact, if you overlay them, they look remarkably similar.
Have you got your answer? For these two charts, we're using data from parts goes back several centuries,
Of course, that doesn't mean but it goes against the perception of cities as being full of pollution and breeding grounds for disease.
"The poisonous germs and pollutions of the city, and endless nuisances." Or more specifically, is there any quantitative data
- It turns out this is something that Geoffrey West pursued He and collaborators like Luis Bettencourt and others
- [Host] They looked at how different properties as the population of the city increases, the data clusters around a straight line
meaning crime grows faster than linear or super linear. you get around 2.2 times as many criminal cases
or around 120% more crime as opposed to the 100% that the same general pattern and even the number of AIDS cases.
but overall, as cities grow larger, So it seems like that medical doctor was onto something. if we all lived in small towns instead,
(mellow music) In 2006, Dirk Helbing, Christian Kuhnert, of gas stations scales as a function of population. as many gas stations?
but energy, gas, for all those cars. you're going to need to double the amount of fuel, they plotted the data on a log log plot
But the exponent wasn't one, it was about 0.8. This means that for every doubling, you only need around 74% (mellow music) The amount of roads and electrical cables
The rough figure that West gives in his book - It is interesting that some of the things on the road, but so can I.
cities can be surprisingly green. than you might think than living out - But cities have even bigger benefits.
and the number of patents all scale superlinearly, with exponents that cluster somewhere around 1.15, you get around 120% more of each.
when you compare a small town of say 50,000 people because infrastructure needs only need to go up by a factor of about 50 while total wages, GDP, patents and inventions,
Unfortunately, disease and crime also go up Or look at it this way, on a per person basis, while you get double all the socioeconomic factors.
they might actually be one of our best inventions and technological progress. that life in the city feels faster.
how fast people walk in cities of different sizes. faster in larger cities. It's not just that the sidewalks are congested or not.
They move faster in cities. but that may come at a cost because as one person put it, "everything nowadays is ultra.
No one knows himself any longer. and then carried away in the world of the times. Could it be that life is accelerating so fast
Well, probably not by Wolfgang von Goethe. For the past 200 years and probably longer,
And yet every generation has managed. to adapt indefinitely. all of us will continue to reap the benefit
that mammals benefit from being larger. where the exponents in biological scaling laws come from, explanatory theory yet.
and 1.15 come from is one of the big goals for theorists. Although even WBE Theory is not universally accepted. doesn't necessarily mean the theory itself is correct.
some of the same scaling exponents, - There's a lot of discussion. And personally, I tend to think it is very impressive.
at University of Vermont, is either not done exactly right that you shouldn't really take this so seriously.
itself might not be true. (mellow music) - In the 1960s, there's a symposium on energy metabolism, and at the end of it, they vote 29 to zero
Because, you know, you got to set some rules. the data does not work. - [Henry] This is a graph of metabolic rate
that looked at 391 species of mammals, And it looks like the three-quarter slope fits quite well. the biggest mammals.
to fall on a line that's closer to two-thirds. you also find a slope that appears closer Could it be that those French scientists
just scale with surface area? (mellow music) For one, many recent studies that are significantly higher than two-thirds.
It generally involves putting animals in a container of their heat production or oxygen consumption, low activity resting state.
to pull off with large animals. where the error bars include both Today, the research community is split.
while others think it's two-thirds. that there is no universal scaling exponent that the metabolic rate of larger mammals
while for smaller ones, it's their mass to the two-thirds. that there are people arguing, and that's good. would be someone to really measure it,
has to be not just one elephant at one zoo, is that scaling laws are real. There are deals to be had.
There's often in real life departures from proportionality, Sometimes things punch above their weight, Sometimes there are detriments to size.
Clearly from an energy efficiency perspective, Similarly, all of us potentially stand It could lead to more discoveries and inventions,
for all of us, which might even give us more heartbeats in our lifetimes. From the surface law to Kleiber's law to WBE theory,
has been one of biology's biggest debates for centuries. there's a good chance to finally put this debate to rest.
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