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Comment by axaxs | Hacker News Reader

I've seen this before and get the gist, but at face value, it's ridiculous. A human who runs every day may expend twice the heartbeats of a sedentary person. He or she will not live half as long, or anything close to it.

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I think the idea is that a frequent runner will have a much lower resting pulse rate, and the “extra” beats they use while exercising will be more than offset by the fewer beats that accumulate during rest?

I haven’t done the math though.

That's the assumption, but I have never seen or done the math either, which is ridiculous because it shouldn't take more than 5 minutes to get some estimates.

Okay, you shamed me into doing it :)

So, this is really rough napkin math, but here goes:

Assuming that...

... a sedentary person (Donald) has a resting BPM of 80.

... an active runner (Justin) has a resting BPM of 60, and a peak BPM of 180 (while running)

If Justin runs for a solid 2 hours, five times a week, he will have

    158*60*60 + 10*60*180 = 676,800 beats per week

While Donald, who doesn't run, but averages 1 hour a week doing strenuous activity, will have

    167*60*80 + 1*60*180 = 812,400 beats per week

Donald's heart beats 20% more often than Justin's. (And that's assuming Donald's heart also peaks at 180.)

(Edited to change names and fix math errors)

Just to be that guy: using two names very similar to eachother (especially for a non-native speaker) is very confusing for examples like this.

Thanks. I actually confused myself when I was writing it. I should have taken that as a sign to change the names. (I was going for a reference[1], but that shouldn't muddle things!)

I hope the new names are differentiated enough.

[1] https://en.wikipedia.org/wiki/Dan_%26_Dave

Thanks for doing the math. I’d say 130-140 would be better than 180 for someone in shape.

Most people can’t even hit 180 after their 20s.

It depends on your goals. If you just want to do the 5K as fast as possible, you'll be close to your max heart rate (180). If you're just "leisure" running (aka. you can talk while running) I suppose 140 is reasonable.

No wonder I dread going to the gym, I find it really strenuous. I'm 37, unfit, and try to hit 180 while running on a treadmill. I was using the same target BPM that I used in college.

Thanks! I'll try 160 BPM next time. Running 45 mins should be more doable.

When I was a runner, I had a resting heart rate in the low 50s. While running I would hover at 180bpm. Now that I’m sedentary (knee accident) I have a heart rate in the 70s.

There are about 10k minutes per week and I ran for about 300 of them. That means my active lifestyle had about 588k beats per week and my sedentary lifestyle has about 750k beats per week. Sedentary life added about 27% total heart rate.

I belive the comparison of heartbeats isn't meant to compare within a species. It works to predict lifespan comparisons between species from total heartbeats.

It's true, and the microscopic theory was done by the same physicist who found the macroscopic relationship, Geoffrey West (one of my personal heroes an current director of the Santa Fe Institute). The theory also explains the upper and lower bounds for the possible size of an animal. If you want to read about it he wrote an amazing book called Scale. I _highly_ recommend it.

OK, I'll add a bit to my previous comment. Is there a limit to how small a mammal can be? If so, what sets the scale?

TL;DR – effective pumping of blood requires precise allowable branching network of capillaries in the circulatory system. At a certain size this network goes from AC to DC and sets the scale for metabolic rate and lifespan in all animals with a circulatory system.

The scale is set by impendance matching of the circulatory system. The heart pumps blood. It is AC. To prevent the AC wave of blood from reflecting back when the capillaries branch out and get smaller, the branching network of the capillaries requires the cross-sectional area of the mother branch to be equal to the sum of the cross-sectional areas of the daughter branches. But when capillaries get too small the heart loses this AC advantage and goes from AC blood wave to purely DC.

So the smallest mammal a shrew has 2 capillary branches, 1 AC, 1 DC. Humans have 8 branches 6 AC then 2 like the shrew 1AC, 1 DC. A blue whale has 15 branches 7 AC then 8 like a human (6 AC then 2 like the shrew 1AC, 1 DC). This branching network sets the smallest length scale of a mammal (actually for any animal that uses blood and mitochondria as its metabolic energy source).

Going back, a shrew has 2 branches 1AC, 1DC. A shrew is 4cm in length and its heart must beat 20 times a second, as nearly all the hearts energy for all animals is expended to push blood through the last small DC branch portion of the capillaries. The shrew must be only 4cm and pump blood with the same pressure and speed as a human (which is the same speed and pressure as a blue whale) through the shrew’s tiny little heart. That is, smaller the animal the larger the metabolic rate. The larger the metabolic rate, the more wear and tear and repair on cells, the shorter the life span.

How are early capillary branches (think of liver network in mammals) and metabolic rate irregularities accounted in this scheme (e.g. average human lives thrice as long and has a metabolism which works twice as fast as in an animal of comparable size)?

I believe the argume is valid for order of magnitude calculations (see Geoffrey West YouTube videos, for an explanation).

+-20 years wouldn't make a difference in a log plot

Why would someone who is very active have an average heart rate double that of a sedentary person?

The idea is that when you're doing strenuous exercise your heart rate is significantly elevated—more than double resting rate. So if you spend hours each day in strenuous exercise (like elite athletes do) your average heart rate could be close to double your resting heart rate. You'd have to exercise a LOT though, and even then it would be difficult to get to double that of a sedentary person, which will be higher than the resting rate of an athlete.

A very fit person will have a resting heart rate of around 50-55BPM, and could have a rate as high as 160BPM or even higher during strenuous exercise. Say they maintain that rate for four hours per day, that brings the average up to around 70. (Actually more since it will be elevated for a while after exercising as well.) Still won't be double though.

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