Monster Pumps

Yesterday’s Science has a long paper on an exciting new scaling law. For a century we’ve known that larger organisms have lower metabolisms, and thus lower growth rates. Metabolism goes as size to the power of 3/4 over at least twenty orders of magnitude:


So our largest organisms have a per-mass metabolism one hundred thousand times lower than our smallest organisms.

The new finding is that local metabolism also goes as local biomass density to the power of roughly 3/4, over at least three orders of magnitude. This implies that life in dense areas like jungles is just slower and lazier on average than is life in sparse areas like deserts. And this implies that the ratio of predator to prey biomass is smaller in jungles compared to deserts.

When I researched how to cool large em cities I found that our best cooling techs scale quite nicely, and so very big cities need only pay a small premium for cooling compared to small cities. However, I’d been puzzled about why biological organisms seem to pay much higher premiums to be large. This new paper inspired me to dig into the issue.

What I found is that human engineers have figured ways to scale large fluid distribution systems that biology has just never figured out. For example, the hearts that pump blood through animals are periodic pumps, and such pumps have the problem that the pulses they send through the blood stream can reflect back from joints where blood vessels split into smaller vessels. There are ways to design joints to eliminate this, but those solutions create a total volume of blood vessels that doesn’t scale well. Another problem is that blood vessels taking blood to and from the heart are often near enough to each other to leak heat, which can also create a bad scaling problem.

The net result is that big organisms on Earth are just noticeably sluggish compared to small ones. But big organisms don’t have to be sluggish, that is just an accident of the engineering failures of Earth biology. If there is a planet out there where biology has figured out how to efficiently scale its blood vessels, such as by using continuous pumps, the organisms on that planet will have fewer barriers to growing large and active. Efficiently designed large animals on Earth could easily have metabolisms that are thousands of times faster than in existing animals. So, if you don’t already have enough reasons to be scared of alien monsters, consider that they might have far faster metabolisms, and also very large.

This seems yet another reason to think that biology will soon be over. Human culture is inventing so many powerful advances that biology never found, innovations that are far easier to integrate into the human economy than into biological designs. Descendants that integrate well into the human economy will just outcompete biology.

I also spend a little time thinking about how one might explain the dependence of metabolism on biomass density. I found I could explain it by assuming that the more biomass there is in some area, the less energy each biomass gets from the sun. Specifically, I assume that the energy collected from the sun by the biomass in some area has a power law dependence on the biomass in that area. If biomass were very efficiently arranged into thin solar collectors then that power would be one. But since we expect some biomass to block the view of other biomass, a problem that gets worse with more biomass, the power is plausibly less than one. Let’s call a this power that relates biomass density B to energy collected per area E. As in E = cBa.

There are two plausible scenarios for converting energy into new biomass. When the main resource need to make new biomass via metabolism is just energy to create molecules that embody more energy in their arrangement, then M = cBa-1, where M is the rate of production of new biomass relative to old biomass. When new biomass doesn’t need much energy, but it does need thermodynamically reversible machinery to rearrange molecules, then M = cB(a-1)/2. These two scenarios reproduce the observed 3/4 power scaling law when a = 3/4 and 1/2 respectively. When making new biomass requires both simple energy and reversible machinery, the required power a is somewhere between 1/2 and 3/4.

Added 14Sep: On reflection and further study, it seems that biologists just do not have a good theory for the observed 3/4 power. In addition, the power deviates substantially from 3/4 within smaller datasets.

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  • > The net result is that big organisms on Earth are just noticeably
    sluggish compared to small ones. But big organisms don’t have to be
    sluggish, that is just an accident of the engineering failures of Earth
    biology. If there is a planet out there where biology has figured out
    how to efficiently scale its blood vessels, such as by using continuous
    pumps, the organisms on that planet will have fewer barriers to growing
    large and active. Efficiently designed large animals on Earth could
    easily have metabolisms that are thousands of times faster than in
    existing animals.

    That is the coolest idea I’ve seen all day.

    But it raises the question: *can* muscles and earth-like biology in general implement continuous pumps? Looking at the ones marked ‘continuous’ in makes them all sound like they require wheels, which is something earth biology also has not been able to make use of in other contexts.

    • That’s a good question.

    • David Percy

      Maybe muscles could use peristalsis to pump continuously. Or maybe several phase-shifted periodic pumps in parallel would act like a continuous pump (like 3 phase alternating current).

    • I can imagine a tube with muscle contractions running down it, sort of like “the wave” at a stadium. Maintaining high pressure might be an issue, though. You could probably get more ideas by looking at propulsion in sea life. Some cephalopods seem to have close to continuous motion using their “wings.”

      But even if you had continuous circulation, there’d still be other problems. Larger organisms have less surface area per unit volume. That makes respiration and heat dissipation trickier. As Robin’s em-city cooling post explains, pipes can solve these problems. That’s a disadvantage for the organism though, as fractal pipes would inhibit movement and be easily damaged. I’m not sure where the tradeoffs would balance out.

      • If surface area relative to volume was a binding constraint, we’d expect to see a power of 2/3. The fact that the power is 3/4 already says that constraint isn’t usually binding.

      • IMASBA

        Surface-volume scaling is the ultimate limit to heat dissipation and nutrent absorption scaling. It’s just that large organisms have developed better mechanisms and live in more suitable environments (cold/wet). Nature has achieved the 3/4 power law because small organisms are not well adapted in these matters. If you build very efficiently cooled small cities you will find that you cannot do better than 2/3 for larger cities.

        I think you’re right that technological innovation will soon surpass anything evolution has come up with.

      • When stuff moves in and out at the speed of light, and is so dense that being a little denser would make a black hole, THEN surface area is an ultimate limit. But before then not so obvious how bit a limit it is.

      • IMASBA

        Long before then you’ll find that whatever improvement you add to something big could also be added to something smaller and that will result in a ~2/3 power law. My point is not that big things can’t be improved, my point is that if you applied those improvements to smaller things as well you can’t do better than 2/3.

        Em “cities” won’t scale with 3/4 because smaller em cities will already be highly optimized, unlike existing small human cities or small biological organisms.

    • jhertzli

      Do bacterial flagella count as wheels?

      • I wouldn’t count them as wheels for the purposes of this discussion because I don’t think the chemical mechanism can ever scale to macro-sized wheels; if they can’t, then there’s no question of evolution doing it or not.

  • Robert Koslover

    This brings to mind a book that I read decades ago that had a nice discussion of the physics/engineering aspects (including some scaling laws, if I recall correctly) of various biological systems.
    “Life’s Devices: The Physical World of Animals and Plants,” by Steven Vogel. See

  • adrianratnapala

    I don’t understand what RH means by “thermodynamically reversibale machinery” in this context, or how to evaluate its energy requirements. Where does RH get his square-root from?

    • Using a quantity of machinery N, the rate of energy use for a rate of production P goes as E = N*P^2. So in the limit of very slow use it costs almost no energy.

  • CommentsCommunicationMajor

    Wouldn’t these massive aliens with high metabolism rates be riddled with cancerous growths?

    • IMASBA

      And/or have shorter lifespans. They’d be like the octopus: intelligent but not living long enough to do much with that intelligence.

      • arch1

        Kind of the polar opposite of (pick your favorite nemesis group), but with a similar outcome.

    • They could have the same meta-cancer solution that whales apparently do.

  • 5ive

    Great post!

  • zachariah priestly

    Biology, could, in fact, ‘invent’ something like this, however, biology is incremental, and is also efficient, meaning that, for instance, a ‘continuous pump’ may require far more energy to run the pump itself, and the blood vessel problem is actually minimal. Further, making a ‘continuous pumping heart’ could be detrimental, requiring its host to constantly be getting food.

    • IMASBA

      Evolution takes time and depends on random events. It most certainly has not cycled through all possible permutations yet and it’s experimenting much more slowly than the human mind and computers are. So we have and will continue to invent solutions that are beyond what evolution has yielded so far. A continuous heart may have the drawback you describe, or it could be advantageous it will take evolution much longer to figure that out than it will take a biotech lab or a computer algorithm (the pumping heart is such an ancient and basic part of all vertebrate life that it will take ages for evolution to alter it into a continuous pump).

  • Tim Tyler

    Human culture is part of biology. Biology won’t soon be ‘over’. Instead, its genetic substrate will change – a genetic takeover. It won’t be the first time that this has happened.

    • I don’t think culture is part biology any more than software is part hardware. They are hugely interrelated, but they’re clearly two separate categories.

      • Tim Tyler

        I never claimed that they were the same category – what I said was that culture is part of biology. Without biology there is no culture. Rocks and stars are examples of things that are not part of biology. Culture is not like that – it is part of living systems.

  • surprised

    Excellent post! Got me thinking: Are there any biological “dual pump”/metabolism systems? E.g. a slow pump for the more sluggish non-brain parts of a body and a fast pump for the less sluggish brain? Such a system, if possible, might bypass some cooling issues.

  • I’m not so sure that a slow metabolism is a terrible thing. After all, something that also correlates with size is lifetime. Large animals live much longer than their smaller compatriots, and probably in a large part due to their slower metabolism. Imagine how much humanity would not have achieved if we all lived to about age 5 before keeling over.

  • J Storrs Hall

    Possibly tangentially related:

    • That analysis is of a very different method of assembly than used by biological systems. Bio systems seem to expand in place, and so don’t need delays to move sub-assemblies to the location where assembly happens. Bio systems construction times seem instead limited by metabolism.

      • J Storrs Hall

        Bio systems need to move food/oxygen from single points of entry to each cell, and waste to points of exit.

    • Gunnar Zarncke

      The rendering of a hypothetical assembler with one-fourth power (Z = 4) scaling law looks a lot like biological systems with “plumbing”:

  • Gunnar Zarncke

    I don’t buy your explanation with pump and sun. If the relationship depended on particular mechanisms the plot would look much different in different areas and domains but it doesn’t. For example plants don’t use cyclic pumps but rather continuous transfer. To me it looks like there is a deeper shared relationship. One idea that comes to mind is one of organizational complexity where more complex life forms build on smaller ones.

    • I agree the pump cycle explanation doesn’t seem to work for plants. But sunlight congestion seems a pretty general density dependence explanation.

      • Gunnar Zarncke

        Yes, but it doesn’t need to be the sun. In general energy sources including food sources need to be transferred and metabolized.
        That would imply that food chains could also fit into this pattern. It would be interesting to look into the metabolism and growth rates of societies of life forms like ants, packs/herds and in the large human societies if different sizes.One prediction would be that a larger society grows slower.

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  • Gunnar Zarncke

    The last incomplete exposition about “thermodynamically reversible machinery to rearrange molecules” reminded me of a 2014 article called “Statistical physics of self-replication” which suggested that bacteria operate near the thermodynamical limit of replication:

    And this together with the congestion idea suggests that energy transfer in biological (and possibly technical systems) may be limited to that scaling law.

  • sanxiyn

    I wonder how dinosaur’s circulation system worked. Did it scale the same way?

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