YT YouTube2Text

YouTube2Text → Transcripts → Why does every mammal get 1 billion heartbeats in their life?

Why does every mammal get 1 billion heartbeats in their life? — Transcript

by Veritasium · 6,580 words · 903 segments · language en · Watch on YouTube

Open in transcriber Summarize with AI Download SRT/VTT

Full transcript

0:00How much LSD should you give an elephant?
0:02(mellow music) Well, to a reasonable person,
0:04the correct answer is probably none.
0:06But what if you needed to do it for a scientific experiment?
0:10In the 1960s, the CIA was working on
0:12a top secret project known as MKUltra,
0:15and one of their main goals was to find out
0:16how drugs like LSD could be used to change human behavior.
0:21And this is where elephants come in
0:23because elephants are normally quite docile,
0:25but sometimes they just snap.
0:27And the hypothesis was
0:29that this change in behavior might be triggered
0:31by the release of an LSD-like substance
0:33that naturally occurs in their brains.
0:36So if that's true, then administering LSD
0:39to a docile elephant might reproduce that behavior.
0:42So the real question was how much LSD should you give
0:45an elephant so that the dose is large enough
0:47to cause a psychological reaction,
0:49but not so large that it causes harm?
0:52(mellow music)
0:52Well, the researchers didn't know, LSD had never been given
0:56to an animal that big,
0:57but they did know that the safe dose in cats
1:00was around 0.3 milligrams.
1:03Now, since an elephant has around
1:04a thousand times the mass of a cat,
1:06they figured we'll give it a thousand times the dose.
1:09They received approval to perform the experiment on Tusko,
1:12an Indian elephant at the Lincoln Park Zoo in Oklahoma.
1:16And there they injected him
1:17with nearly 300 milligrams of LSD.
1:20But within five minutes, Tusko trumpeted, collapsed,
1:24fell heavily onto his right side, defecated,
1:27and went into status epilepticus.
1:30They administered a few other drugs
1:32in an attempt to revive him,
1:33but Tusko died shortly thereafter.
1:36The mistake they made was to assume
1:38that safe drug dosage scales linearly with mass.
1:42It does not.
1:43And it turns out there are a lot of things like this
1:46that don't scale in the way you'd expect.
1:48(mellow music)
1:49For example, take the smallest mammal by mass,
1:52the Etruscan shrew,
1:53and the largest land mammal, the African bush elephant.
1:57Which do you think has more heartbeats
1:59over the course of its entire life?
2:01Well, an African elephant has
2:03around a billion heartbeats in its lifetime,
2:06and an Etruscan shrew also has a billion
2:09heartbeats in its lifetime.
2:11What about a wallaby?
2:13Also a billion.
2:14A two-toed sloth?
2:15A billion again.
2:16Just about every mammal, no matter
2:18what environment they live in, how large they are,
2:21or even whether they live for one year or 100 years,
2:24they all get around a billion heartbeats
2:27between the day they're born and the day they die.
2:29- Why a billion?
2:30Why not a million?
2:31Why not a thousand?
2:32It's not these other numbers.
2:33- That is every mammal except one.
2:37This video is in large part based on the book
2:39Scale by Geoffrey West.
2:41If you want to learn more,
2:42I'll put a link to it down in the description.
2:44What's even more curious is that
2:46just by knowing a mammal's mass,
2:48you can predict a staggering number
2:50of biological traits from its pulse rate
2:52and reproductive output to its total lifespan.
2:56The same pattern holds for cities.
2:58If you know the population and location,
3:00that allows you to forecast everything from average wages
3:02and patent filings to crime rates, disease prevalence,
3:06and even the literal speed at which pedestrians walk.
3:10So how is that possible?
3:12Well, for that, we have to go back to the case
3:13of Tusko the Elephant.
3:15Researchers assumed that safe drug dosage
3:17is proportional to mass.
3:19Double the mass, double the dose.
3:20But it turns out that the speed at which an animal
3:23can process chemical compounds
3:24doesn't depend directly on its mass.
3:27It depends more on its metabolic rate.
3:29That is the number of calories it uses
3:32in a given amount of time.
3:33- There's a lot going on in your body.
3:35Your heart is pumping, that takes energy.
3:38You're moving food around.
3:40Digestion takes energy.
3:42Keeping your brain going takes energy, breathing.
3:44Everything that you do requires energy.
3:47(mellow music) - [Host] For a cat, for a single day,
3:49they require roughly 250 kilocalories of energy,
3:53used by all of their trillions of cells.
3:56But there is nothing special about a cat's cells.
3:59If you take a cat's cells and an elephant's cells
4:01and put them under a microscope,
4:02you'll find they're a similar size, similar makeup,
4:05and they perform the same sorts of functions.
4:07The same is true for other animals.
4:10In other words, the building blocks
4:11of animals are always roughly the same.
4:14So an elephant that has a thousand times the mass
4:16has about a thousand times as many cells.
4:18So you'd expect it would need a thousand
4:21times as much energy.
4:22So 250,000 kilocalories per day.
4:26But that is where you run into problems.
4:28- So what's the issue here?
4:30If I'm an organism
4:31and I'm burning up energy all day long,
4:33that energy is radiated out in the form of body heat.
4:37So we're constantly losing heat through our surface,
4:40through our skin, to the environment.
4:43- To see why this matters, let's simplify the problem
4:46and do the standard physicist thing.
4:47Let's assume our animals are perfect spheres.
4:51To be clear, this isn't necessary for the argument to work,
4:53but it does make everything a lot easier to follow.
4:56Since the volume of an animal is proportional to its mass,
4:59our 3000 kilogram elephant has a volume a thousand times
5:02greater than our three kilogram cat.
5:04So its radius must be 10 times larger.
5:06That's because volume is proportional to radius cubed.
5:10But surface area only grows as radius squared.
5:13So the elephant's surface area
5:14only increases by a factor of 100.
5:17Generating a thousand times as much heat
5:18while only having a hundred times the surface area
5:20to radiate it away would end very
5:23poorly for the elephant.
5:24If this were the case, it would boil alive.
5:28(mellow music) So in 1838,
5:30French scientists proposed a different scaling law.
5:32Since metabolism generates heat
5:34and that heat is radiated through the surface,
5:36metabolic rate or B, should scale in proportion
5:39to the surface area, A, instead.
5:42This became known as the surface law.
5:44Now, we can rewrite this to see
5:46how metabolic rate scales as a function of mass.
5:48Surface area is proportional to radius squared,
5:51so we can swap that in,
5:52and if mass is proportional to radius cubed,
5:55then radius must be proportional to mass to the one-third.
5:58Plugging that in for R,
5:59we find that metabolic rate should scale
6:00with mass to the two-thirds.
6:02- Really familiar example would
6:04come from thinking about cooking.
6:07(mellow music)
6:07Maybe you want to make a big turkey for Thanksgiving.
6:10People commonly phrase it as how long do I need per pound?
6:13But that you realize is linear thinking.
6:15The important thing is really the thickness of the bird
6:18or the roast, because the heat is coming in
6:21by conduction from the oven
6:24and it's got to do thermal diffusion into the meat.
6:28The time for the diffusion will scale
6:30like the characteristic length,
6:32which in this case would be the thickness of the meat.
6:34It'll go like the dimension squared,
6:37whereas volume of the meat is going to be like length cubed,
6:41and that's proportional to the weight
6:43of the bird or the roast.
6:44So when you put those things together,
6:46you'll get that the characteristic amount of time needed
6:48to cook the roast will go like its mass
6:51to the two-thirds power.
6:52- So if I'm thinking about cooking a roast
6:55that weighs twice as much as another roast, how much longer?
6:58Is that two to the two-thirds the time?
7:01- Yeah, if you wanted to double the weight,
7:03then you only have to cook it about 60% longer,
7:06not 100% longer.
7:08- [Host] Similarly, according to this scaling,
7:11an elephant that's a thousand times as heavy as a cat
7:13should only burn a hundred times as many calories.
7:16So 25,000 instead of 250,000.
7:19And the appropriate dose of LSD for Tusko
7:22would've been just 30 milligrams.
7:25These two wildly different predictions come from different
7:27assumptions about how metabolic rate
7:29scales as a function of mass.
7:31But notice in both cases, it's just proportional
7:34to mass raised to some power.
7:36These kinds of relationships are called power laws
7:38and all power laws have a special property.
7:41If you take the logarithm of the X and Y values,
7:44you get a straight line.
7:45And the slope of the line is equal
7:47to the exponent of the power law.
7:49This makes it easy to identify
7:51different types of power laws.
7:52If the slope is one, that's just everyday linear scaling.
7:55If it's less than one, like the surface law,
7:58that is called sublinear scaling.
8:00And if it's larger than one,
8:01that is known as superlinear scaling.
8:04For nearly a hundred years, biologists generally agreed
8:07that the two-thirds exponent
8:09of the surface law was the correct one for metabolic rate.
8:12But then in 1932, Swiss biologist, Max Kleiber,
8:16decided to put it to the test.
8:17He took the metabolic rates
8:19of different animals from a small dove at 150 grams
8:22to a large steer at 680,000 grams,
8:26and then he plotted them against their mass
8:28on a log log plot.
8:29And as expected, all the data did fall on a straight line.
8:32But the slope wasn't two-thirds.
8:35Instead, it was about three quarters.
8:37This became known as Kleiber's Law.
8:40It implies that if you double an animal's mass,
8:42metabolic rate goes up by about 1.68,
8:45an increase of 68% instead of the 59%,
8:49which would be predicted by the two-thirds scaling law.
8:51So according to Kleiber's Law,
8:53an elephant burns roughly 178 times
8:56as many calories as a cat, or about 45,000 kilocalories.
9:00And the actual LSD dose Tusko should have received
9:03was 53 milligrams, which is around a sixth of the dose
9:06the researchers gave him.
9:08So that explains the dosing catastrophe
9:10with Tusko The Elephant.
9:13(mellow music)
9:13Kleiber's original work was based on a small data set,
9:16primarily made up of mammals.
9:18But if you plot the data for a larger range of mammals,
9:21as well as for other animals
9:22like birds, reptiles, and fish,
9:24you find that they all follow
9:25roughly the same scaling relationship.
9:27Now, they don't all fit perfectly onto the same line
9:29because the base metabolic rate
9:31for warm-blooded animals is higher
9:32than for cold-blooded ones,
9:34but they all scale according to the same power law,
9:37mass raised to the three-quarters.
9:39Some argue that this relationship expands all the way down
9:42to single cells and the molecular machines inside of them.
9:45If that's true, Kleiber's Law governs life
9:47spanning more than 25 orders of magnitude.
9:51But then the question is,
9:53if an elephant has so many more cells
9:56and each cell is a similar size
9:58to a cell in a smaller creature,
10:00and yet it's using proportionately less energy,
10:05like it's got a lower metabolic rate per pound
10:08or per kilo or per cell,
10:10that's really saying that those cells
10:13are functioning with much less energy.
10:15- It's like there's some efficiency to being big,
10:18and it's hard to understand why.
10:20What is it that the cells are providing to each other,
10:24somehow cooperating in some way?
10:26- I just put in my calculator 100 to the three quarters,
10:29so if you got an organism that's 100 times bigger,
10:32then according to this, only 31.6
10:35times the metabolic rate.
10:37So it seems like a big savings.
10:40- It's a massive improvement, right?
10:42It's a big savings.
10:43It's a biological fact,
10:44but people have been arguing now for a century
10:48what accounts for this three quarters.
10:50(mellow music)
10:50- In the decades following Kleiber's observation,
10:52the mystery only deepened.
10:54Researchers discovered that brain size also roughly scales
10:58as mass to the three quarters,
10:59and so does an animal's growth rate
11:01and the amount of blood pumped per minute.
11:04But not every property scales as mass to the three quarters.
11:07- If you ask how long a creature will live, a mammal,
11:11that tends to be proportional to its mass
11:13to the one quarter power.
11:15One over four, not three over four.
11:18- [Host] So that means if you double the mass of a mammal,
11:20then on average, its lifespan is around 19% longer.
11:24Similarly, blood circulation time also scales
11:26as roughly mass to the one quarter, while breathing rate
11:29and heart rate both scaled to the negative one quarter.
11:32They're not all three quarters power laws,
11:35but they are all multiples of a quarter.
11:37So the question on everyone's mind was
11:40where are these quarter power scaling laws coming from?
11:43- One popular theory emerged in the 1990s.
11:47(mellow music) Brian Enquist was studying
11:48for an undergraduate degree in biology.
11:50- Most of the biology classes then that you take,
11:53you learn about the Krebs Cycle
11:55and then you have to memorize all the different parts
11:57of a flower and then all...
11:59They have a different terminology for everything.
12:00- [Henry] But then one day he took a zoology class
12:03where they showed him those quarter power scaling plots.
12:05- [Brian] I just couldn't believe it.
12:07I was like, "You got to be kidding me."
12:09You know, this is kind of like something fundamental
12:11that's kind of like underlying biological diversity.
12:14And there I knew immediately that I wanted
12:17to kind of quit my specialized
12:19kind of plant physiology research
12:21and do something associated with scaling.
12:24(mellow music)
12:24- [Henry] So Enquist started studying for his PhD,
12:27under Professor James Brown,
12:29who had been thinking about scaling laws for years.
12:31So they knew that often when power laws appear,
12:34there's some form of self-similarity
12:35in the underlying system.
12:36So they wondered, what could that self-similarity be?
12:39And they suspected that it might have something to do
12:41with the way resources are transported through the body,
12:44specifically the networks that do this.
12:46They had the biological intuition,
12:48but to get a complete theory,
12:49they needed a formal mathematical framework.
12:52In other words, they needed a mathematician
12:54or a theoretical physicist.
12:55- And at the time, Jim was associated
12:58with the Santa Fe Institute,
13:00and he started asking around with,
13:02is there anyone up here that's interested in these
13:04biological scaling relationships?
13:06And then the president at the time said, "You know what?
13:08I know of this physicist who's up at Los Alamos
13:12who was talking about biological scaling relationships."
13:15And so we met Geoffrey and it was like immediately,
13:18it's like we'd been talking about the same things
13:21for like years.
13:22It's like, you know, finding,
13:25someone who's been like speaking your language,
13:27but no one could understand you.
13:28- [Henry] So West, Brown and Enquist teamed up
13:30to try and find a compelling explanation for Kleiber's Law.
13:33- They started by assuming three simple premises.
13:37The first premise is that the networks
13:39that distribute resources are space-filling,
13:41since they need to reach every cell in the body.
13:44The second premise is that the terminal units
13:46of those networks, the thinnest segments
13:48on the outer periphery of the delivery system,
13:50have the same width regardless of the size of the organism.
13:53That is the outermost blood vessels that carry nutrients
13:56to an elephant's skin cells are about as thick
13:58as the ones in a mouse.
14:00The elephant just has many more of them.
14:02And the third premise is that over time,
14:04evolution has driven these transport networks
14:06toward an efficient design.
14:08So what should such a network look like?
14:11(mellow music)
14:11Well, intuitively, to get fuel from one place to another
14:14as efficiently as possible,
14:15you want the path to be as short as possible.
14:17So basically a straight line.
14:18But because fuel needs to reach every part of the body,
14:21you would also need many different paths.
14:23And as you go to larger and larger organisms,
14:25the networks inside need to
14:27reach a larger and larger volume.
14:29One way to do this is to stretch all the paths
14:31and match the growth of the animal.
14:33In this case, the volume of the animal
14:35should scale as these internal path lengths cubed.
14:38Or if we rearrange that, internal path length should scale
14:40as volume to the one-third,
14:42just like the overall length of the animal does.
14:45But this design is incredibly wasteful.
14:47Take these two regions.
14:49The two vessels that are bringing blood here
14:51go through almost the same path in the body,
14:53and they only split up just
14:55before they reach their destinations.
14:57If instead we had just one vessel up to this point
14:59and split it only when the paths needed to diverge,
15:02we could serve the two regions
15:03using a lot less vessel material
15:05and a lot less blood to fill the vessels.
15:07Of course, you can extend this logic
15:09for all the blood vessels in the body,
15:10and you end up with a much more efficient design
15:13of branching blood vessels.
15:15But now we run into another issue
15:17because each branching point provides an opportunity
15:19for some of the blood to bounce back, that is reflect.
15:22If you have many reflections,
15:24that would mean it costs significantly more
15:25energy to pump blood around.
15:27So next, they argue that nature should favor structures
15:30that minimize reflections.
15:31And as it turns out, this happens
15:33if the cross-sectional area of the vessels
15:35stays the same before and after the branching.
15:37So if you've got a cross-sectional area
15:39of two centimeters squared for the main vessel,
15:41then each of the two branches need to have an area
15:43of one centimeter squared each, for large vessels at least.
15:47For smaller ones, daughter branches can be a bit thicker
15:50to allow blood to slow down
15:52and exchange resources with the tissue it's reaching.
15:55If you keep repeating this pattern across the network,
15:57you end up with this, a branching self-similar fractal.
16:01And if you look at the actual shape
16:03of the circulatory system, it has this geometry.
16:06So it seemed like they were onto something.
16:09- But how do you get from this
16:11to quarter power scaling laws?
16:13Well, mathematician Felix Hausdorff discovered
16:15that self-similar fractals have an interesting property.
16:18(mellow music) Take a straight line segment.
16:19It's completely one-dimensional and not a fractal at all.
16:22Hausdorff assigned this line segment a value of 1.0.
16:26But now imagine adding a few bends
16:29and more bends to those bends.
16:31If you keep doing this, the line becomes more
16:33and more fractal-like.
16:35Eventually, if you keep applying
16:36the right kind of contortions,
16:38that one-dimensional line segment fills up
16:40an entire region of the 2D plane.
16:42Hausdorff assigned these space-filling fractal curves
16:45a value of 2.0, corresponding to their dimensionality.
16:48The same ideas apply to a 2D surface.
16:51- So think about a piece of paper, right?
16:53Two-dimensional.
16:55All then the fractal network is doing is crumpling up
16:58that sheet of paper, and it effectively fills
17:01a ball of volume.
17:02So you can now describe that sheet of paper
17:05as a sphere instead of a two-dimensional sheet of paper.
17:09- [Henry] Repeat the right pattern of folds
17:10at smaller and smaller scales, and a 2D surface
17:13fills more and more of a 3D volume.
17:15In the mathematical limit, it becomes space filling
17:18with Hausdorff dimension of 3.0.
17:20- [Brian] You know, biologically, I said,
17:22"Well, what does that mean?"
17:23That enables an organism for a given size
17:26to pack in more of these metabolic surface areas
17:30than would be expected.
17:32And it's because of this fractal-like structure
17:35that enables you then to pack in and have all of these folds
17:38and convolutions and on top of each other
17:41to pack in an enormous amount of membrane surfaces.
17:44- As a result, the Hausdorff dimension of the surface
17:47of the circulatory system is roughly three,
17:50meaning its surface area doesn't scale
17:52as its length squared, but it's length cubed.
17:55And since the metabolic rate hinges on
17:57how fast resources can be exchanged across the surface area,
18:00well, it must also scale like length cubed.
18:03But remember, West, Brown and Enquist
18:05wanted to explain Kleiber's Law.
18:07So they needed to know how metabolic rate scales with mass.
18:12(mellow music)
18:12Since every cell needs to be served by the network,
18:14this means that the volume
18:15around the network should be proportional
18:17to the animal's mass.
18:18And since volume is just surface area times length
18:21and surface area is proportional to length cubed,
18:23that means both volume and mass
18:25must be proportional to length to the fourth,
18:28which can be rewritten to show that length is proportional
18:30to mass raised to the one quarter.
18:33And if you plug that into the equation
18:34for the metabolic rate,
18:35you find that the metabolic rate
18:36must be proportional to mass to the three-quarters,
18:40exactly as Max Kleiber had found.
18:43West, Brown and Enquist published their work in 1997,
18:46and it soon came to be known
18:48as WBE Theory, after their initials.
18:50- And the theory is quite rigid.
18:53It makes very specific predictions.
18:55This is good science.
18:57Okay?
18:57This is sticking your neck out,
18:59and it's an incredibly beautiful theory.
19:02(mellow music) - [Derek] Take a look at this table
19:03from Geoffrey West's book.
19:04These are the scaling exponents WBE theory predicts,
19:07including many that are not multiples of a quarter,
19:10but all follow from the same theory.
19:12For example, the radius of an animal's aorta
19:15should scale with its mass to the three-eighths or .375.
19:18And the area of its lungs should scale with mass
19:21to the 11-12ths or about 0.92.
19:24In total, this chart makes 26 different predictions.
19:27Now, these are the observed data.
19:30Radius of the aorta, 0.36.
19:32Lung area, 0.95.
19:35- [Steven] That's the really shocking thing
19:37about what they did.
19:37They had a table with something like, I don't know,
19:3920 or 30 predictions of exotic exponents,
19:43and that's what you really see in the data.
19:45So this one theory accounts not only
19:46for the three-quarters power of metabolism,
19:49but for literally dozens of other things
19:51that biologists have measured.
19:53- Some of the scaling laws are easy to explain
19:56once you've got the three-quarters law for metabolism.
19:58Take a mammal's heart rate, for instance.
20:01Heart rate is equal to the blood flow rate
20:03over the amount or volume of blood in every beat.
20:05(mellow music)
20:06The volume of blood per beat has been found
20:08to scale in direct proportion to an animal's mass.
20:10So that's just M.
20:11And the blood flow rate?
20:13Well, remember that metabolism is all about
20:15how nutrients get distributed around the body.
20:17So most biologists agree metabolic rate
20:19and blood flow rate are directly
20:20proportional to one another.
20:22So heart rate should scale as metabolic rate over mass.
20:25Swapping in the scaling law Kleiber had found,
20:28that gives us M to the minus one quarter,
20:30meaning bigger animals should have slower
20:32heartbeats than smaller ones.
20:34And this is exactly what we observe in nature.
20:36The world's smallest mammal, the Etruscan Shrew,
20:39has an extraordinary heart rate of 1200 beats per minute.
20:42That's 20 beats per second.
20:44Whereas the biggest land mammal, the African bush elephant,
20:47has a typical heart rate of only 30 beats per minute.
20:50And we can do something similar for lifespan.
20:53One of the leading theories is
20:54that an animal's lifespan is based on
20:56the accumulation of metabolic damage.
20:58That is, as each chunk of tissue in an organism
21:01processes nutrients over time,
21:03this causes damage to accumulate,
21:05and that over time causes the animal to die.
21:08So the rate at which an animal accumulates damage
21:10is its metabolic rate per unit of mass,
21:12and its lifespan should be the inverse of that rate.
21:15If damage accumulates faster, it dies sooner.
21:17If it accumulates slower, it lives longer.
21:20So lifespan is proportional to M over B,
21:23or substituting in Kleiber's Law, M to the one quarter.
21:27So lifespan should increase with mass.
21:30And you do see this in nature.
21:31(mellow music)
21:31A shrew only lives for one to two years in the wild
21:34while a mighty African elephant can live up to 70 years.
21:38So if you're a small mammal,
21:39you have many heartbeats per minute,
21:41but you live a relatively short life.
21:43Conversely, if you're a larger mammal,
21:45your heart beats much slower and you live a lot longer.
21:48- So it's the, you know, live fast and burnout
21:52and die young, right?
21:54Or spend it frugally and live a really long life.
21:57- But you might have also noticed something else.
22:00Heart rate scales as B over M.
22:02So it equals B over M times some constant.
22:05And lifespan scales as M over B.
22:08They're inverses of each other.
22:09They scale in equal and opposite directions.
22:12Now, the total number of heartbeats in an animal's life
22:15is just the heart rate multiplied by the lifespan.
22:17So when you multiply these two terms, they cancel out,
22:20leaving you with just a constant.
22:22So that suggests that no matter
22:24what mammal you're talking about,
22:26it should have roughly the same number of heartbeats.
22:29You can find that number by just plugging in some examples.
22:32Let's start with the Etruscan Shrew.
22:35The shrew's 1200 beats per minute multiplied by a lifespan
22:37of around 1.5 years gives you
22:39around 950 million heartbeats
22:41in the course of the shrew's life.
22:43Meanwhile, an African elephant's 30 beats per minute
22:45multiplied by a lifespan of around 65 years
22:47gives you a little over a billion heartbeats.
22:51And we could keep going.
22:52(upbeat music) But for nearly every mammal you look at,
22:54you keep landing at the same figure of
22:56around a billion heartbeats.
22:58This is why nearly every mammal from a tiny field mouse
23:01to a gazelle, from a cheetah to a hippopotamus,
23:05they all get around a billion heartbeats
23:07between the day they're born and the day they die.
23:12But there is one major outlier, one mammal
23:15that gets significantly more than a billion heartbeats.
23:18And that is us, humans. (mellow music)
23:21We are the lucky ones.
23:23Three centuries ago, humans were much closer
23:26to the standard value of one billion heartbeats.
23:28But around the mid 1800s, germ theory
23:31and better sanitation methods became widespread,
23:33causing a stark decrease in the number of child mortalities
23:36and deaths from disease.
23:37So life expectancy began to climb up.
23:39And with it, the average number of heartbeats in a lifetime.
23:42If you look closely, you can also see some significant drops
23:46like this 1918 dip from the Spanish flu pandemic
23:49or over here, what appears to be
23:50the impact of the Second World War.
23:52But overall, the trend is clear.
23:54We have systematically been increasing the number
23:57of heartbeats we get in our lifetime to the point
23:59where now the average human gets nearly three billion
24:02heartbeats before they die.
24:05I don't know if there's a better argument for science
24:07and technology than this.
24:09It has literally given the average human
24:11more than a full extra life.
24:13And it's not just humans.
24:14Other mammals have been observed
24:16to have much longer lives in captivity when they're away
24:18from the hazards they would naturally encounter in the wild.
24:22Or if you look at it purely from the number of years we get,
24:24we now have the lifespan of a much larger mammal,
24:27somewhere between an elephant and a whale.
24:31But there is one curious thing about this trend.
24:33(mellow music) Take a look at this graph.
24:35It looks surprisingly similar to the graph from before.
24:38In fact, if you overlay them, they look remarkably similar.
24:41Now I want you to take a guess at what this graph is.
24:44Have you got your answer?
24:46It is the number of people living in cities.
24:49For these two charts, we're using data from parts
24:52of the United Kingdom where the record keeping
24:54goes back several centuries,
24:56but the rest of the world has followed similar trends.
24:59Of course, that doesn't mean
25:00cities cause people to live longer,
25:03but it goes against the perception of cities
25:05as being full of pollution and breeding grounds for disease.
25:09Already in 1889, a medical doctor wrote,
25:12"The poisonous germs and pollutions of the city,
25:14it's impure air and water, bad sewage,
25:17and endless nuisances."
25:19So how do you reconcile these two views?
25:22Or more specifically, is there any quantitative data
25:25on how smaller cities compare to larger ones?
25:28- It turns out this is something that Geoffrey West pursued
25:31after his work with Brown and Enquist.
25:33He and collaborators like Luis Bettencourt and others
25:37have looked at scaling laws in cities.
25:39(mellow music)
25:39- [Host] They looked at how different properties
25:41like the amount of crime scale
25:43as the population of the city increases,
25:45and what they found is that if you plot
25:46serious crimes on a log log plot,
25:48the data clusters around a straight line
25:50with a slope of 1.15,
25:52meaning crime grows faster than linear or super linear.
25:56So for every doubling of a city's population,
25:59you get around 2.2 times as many criminal cases
26:02or around 120% more crime as opposed to the 100%
26:07you might naively expect.
26:08To make matters worse, researchers found
26:10that the same general pattern
26:11holds for the amount of wastewater
26:13and even the number of AIDS cases.
26:16The exact exponents vary a little,
26:18but overall, as cities grow larger,
26:20you systematically get more of each.
26:23So it seems like that medical doctor was onto something.
26:26And you might think life on earth would be better off
26:28if we all lived in small towns instead,
26:31but that might not be the case.
26:33(mellow music) In 2006, Dirk Helbing, Christian Kuhnert,
26:36and Geoffrey West looked at how the number
26:38of gas stations scales as a function of population.
26:41- If a city is twice as big, does it need twice
26:44as many gas stations?
26:45Because, you know, we have to supply not exactly nutrients,
26:48but energy, gas, for all those cars.
26:51- [Host] The naive expectation is that
26:53if you double the number of cars,
26:54you're going to need to double the amount of fuel,
26:56so double the gas stations.
26:58To find out whether this was true,
26:59they plotted the data on a log log plot
27:01and found a straight line.
27:03But the exponent wasn't one, it was about 0.8.
27:07This means that for every doubling, you only need around 74%
27:11more gas stations, which is a decent savings.
27:14(mellow music) The amount of roads and electrical cables
27:17also scale in roughly the same way.
27:19The rough figure that West gives in his book
27:21is that they all have scaling exponents of around 0.85.
27:23- It is interesting that some of the things
27:25that we can share, like you can drive
27:28on the road, but so can I.
27:29When it's shared resources, yes,
27:32cities can be surprisingly green.
27:34The argument is that cities can be even greener
27:36than you might think than living out
27:38in the middle of nowhere.
27:39- But cities have even bigger benefits.
27:42Things like total wages, GDP,
27:44and the number of patents all scale superlinearly,
27:47with exponents that cluster somewhere around 1.15,
27:51meaning that for every doubling in size,
27:53you get around 120% more of each.
27:57All of this becomes especially significant
27:59when you compare a small town of say 50,000 people
28:01to a city 100 times its size
28:04because infrastructure needs only need to go up by a factor
28:06of about 50 while total wages, GDP, patents and inventions,
28:11they all go up by a factor of 200.
28:13Unfortunately, disease and crime also go up
28:16by the same factor.
28:18Or look at it this way, on a per person basis,
28:21you'd only need about half the infrastructure,
28:23while you get double all the socioeconomic factors.
28:27So cities far from being detrimental to the world,
28:29they might actually be one of our best inventions
28:32and an indirect driver of a lot of scientific
28:35and technological progress.
28:36Perhaps this is also why people often say
28:38that life in the city feels faster.
28:41A feeling that seems justified
28:42because researchers looked at
28:44how fast people walk in cities of different sizes.
28:47And they found that people literally do walk
28:49faster in larger cities.
28:51- That turns out to depend on city size.
28:54It's not just that the sidewalks are congested or not.
28:57It's just like the vibe gets people amped up.
29:00They move faster in cities.
29:02- So the pace of life seems to be increasing,
29:05but that may come at a cost
29:07because as one person put it, "everything nowadays is ultra.
29:11Everything is being transcended continually
29:13in thought as well as in action.
29:14No one knows himself any longer.
29:16Young people are stirred up much too early in life
29:19and then carried away in the world of the times.
29:21Wealth and rapidity are what the world admires".
29:24Could it be that life is accelerating so fast
29:26that humans won't be able to keep up?
29:29Well, probably not
29:30because this quote was written in 1825
29:32by Wolfgang von Goethe.
29:34For the past 200 years and probably longer,
29:38almost every generation has felt like life was accelerating.
29:41And yet every generation has managed.
29:43So I think it's likely we can continue
29:45to adapt indefinitely.
29:47And as cities continue to grow in size,
29:50all of us will continue to reap the benefit
29:52of economies of scale in much the same way
29:54that mammals benefit from being larger.
29:57But while WBE Theory seems to predict
29:59where the exponents in biological scaling laws come from,
30:02for cities, there is no widely accepted
30:04explanatory theory yet.
30:06Trying to explain where those exponents of 0.85
30:09and 1.15 come from is one of the big goals for theorists.
30:12Although even WBE Theory is not universally accepted.
30:16For one, the fact it predicts the right exponents
30:19doesn't necessarily mean the theory itself is correct.
30:22There are a few other theories that predict
30:24some of the same scaling exponents,
30:26and there are also some other critiques.
30:29- There's a lot of discussion.
30:31It may look convincing.
30:32And personally, I tend to think it is very impressive.
30:35But I have very good colleagues like Peter Dodds
30:37at University of Vermont,
30:39and he thinks that a lot of the data analysis
30:41is either not done exactly right
30:43or that the data are so noisy
30:46that you shouldn't really take this so seriously.
30:49- Dodds even argues that Kleiber's Law
30:51itself might not be true. (mellow music)
30:53- In the 1960s, there's a symposium on energy metabolism,
30:59some name like this in animals,
31:02and at the end of it, they vote 29 to zero
31:04that it's going to be three quarters, right?
31:06Because, you know, you got to set some rules.
31:09If you go back and look at the data,
31:10which no one is really doing anymore, right,
31:12the data does not work.
31:13Like it doesn't work.
31:15(mellow music)
31:15- [Henry] This is a graph of metabolic rate
31:17as a function of mass based on a study
31:19that looked at 391 species of mammals,
31:22much larger than Kleiber's range.
31:23And it looks like the three-quarter slope fits quite well.
31:26But this is just the top part of the chart,
31:28the biggest mammals.
31:30If you zoom out, you see that the rest of the mammals appear
31:32to fall on a line that's closer to two-thirds.
31:36And in recent studies of bird metabolism,
31:38you also find a slope that appears closer
31:40to two-thirds than three-quarters.
31:42Could it be that those French scientists
31:44from centuries ago were right,
31:45that metabolic rate really does
31:47just scale with surface area?
31:48Well, not so fast.
31:51(mellow music) For one, many recent studies
31:52of cold-blooded animals find slopes
31:54that are significantly higher than two-thirds.
31:56The bigger problem is that measuring
31:58metabolic rates is difficult.
31:59It generally involves putting animals in a container
32:02and taking very precise measurements
32:03of their heat production or oxygen consumption,
32:06all while ensuring that the animal is in an unstressed,
32:09low activity resting state.
32:10Unsurprisingly, this is particularly difficult
32:13to pull off with large animals.
32:15And as a result, many studies have found scaling exponents
32:17where the error bars include both
32:19two-thirds and three-quarters.
32:22Today, the research community is split.
32:24Many uphold Kleiber's Law and the three-quarter scaling,
32:26while others think it's two-thirds.
32:28But a growing number suspect
32:29that there is no universal scaling exponent
32:32across all of life.
32:33In fact, it may very well be the case
32:35that the metabolic rate of larger mammals
32:37scales as their mass to the three-quarters,
32:39while for smaller ones, it's their mass to the two-thirds.
32:41- You know, it's like everything in science
32:43that there are people arguing, and that's good.
32:45- I guess the bigger exhortation
32:47would be someone to really measure it,
32:49measure things beautifully.
32:50You know, we're in 2026,
32:52has to be not just one elephant at one zoo,
32:55it needs to be measured again really well.
32:57- [Host] What everyone does agree on
32:58is that scaling laws are real.
33:00- Life is not linear all the time.
33:03There are deals to be had.
33:04There's often in real life departures from proportionality,
33:08and you have to be aware of it.
33:10Sometimes things punch above their weight,
33:12and as you get bigger, you get more efficient.
33:15Sometimes there are detriments to size.
33:18- So it pays to know how things scale.
33:21Clearly from an energy efficiency perspective,
33:23animals benefit from being larger.
33:26Similarly, all of us potentially stand
33:28to gain from having more people living in larger cities.
33:31It could lead to more discoveries and inventions,
33:34and in doing so, improve the standard of living
33:36for all of us, which might even give us more
33:39heartbeats in our lifetimes.
33:44From the surface law to Kleiber's law to WBE theory,
33:48how metabolic rate scales with mass
33:50has been one of biology's biggest debates for centuries.
33:52By collecting better data and analyzing it carefully,
33:55there's a good chance
33:56that the next generation of researchers could be the ones
33:58to finally put this debate to rest.
34:00It could be one of you watching or a student that you know.
34:04And today's sponsor, Brilliant, is helping
34:06to train the next generation of researchers,
34:08preparing their minds to solve the huge
34:10questions they'll face.
34:11Brilliant is a cutting edge personal tutor
34:13that helps any student excel in math, science, and coding.
34:17When it comes to learning,
34:19one-on-one tutoring really is the gold standard,
34:21but this can be expensive and logistically difficult.
34:24As a substitute, students often turn to AI for guidance.
34:28But most AI platforms hinder learning
34:30by simply just giving away the answers.
34:33So instead, Brilliant is designed to guide students
34:36to their own aha moments by asking probing questions
34:39and by breaking problems down step by step.
34:42For instance, check out what happened when I launched one
34:44of Brilliant's lessons on rotating coordinates
34:46and told its tutoring tool that I was struggling.
34:49It asked me a specific follow-up question
34:51and even labeled relevant points on the graph
34:54to give me a nudge.
34:55Brilliant is an excellent aid for the young math
34:58and science learners in your life.
34:59It's the kind of tool I wish I had when I was in school.
35:03So click the link below or scan the QR code
35:06to get started with Brilliant's tutor for free,
35:08or upgrade to premium to unlock all courses.
35:11And right now, Veritasium viewers can save 20% off
35:14an annual subscription at brilliant.org/veritasium.
35:18So I want to thank Brilliant for sponsoring this video,
35:20and I want to thank you for watching.

About this transcript

This page contains the full transcript of Why does every mammal get 1 billion heartbeats in their life? by Veritasium, generated from the public captions YouTube serves with the video. The transcript has 6,580 words across 903 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

What you can do with it

Use the transcript to take notes, quote the speaker, build a study guide, generate a summary with ChatGPT or Claude via the YouTube Summary tool, or export it as a timed subtitle file with YouTube to SRT. You can also re-open it in the transcriber to translate the transcript into 100+ languages.

Free YouTube transcript tool

YouTube2Text is a free YouTube transcript generator — no signup, no daily limit. Paste any YouTube link and get the full transcript instantly, with timestamps, click-to-jump, translation to 100+ languages, AI prompts for ChatGPT, Claude, and Gemini, and exports to TXT, SRT, VTT, or Markdown.