In 1932, the zoologist Max Kleiber noticed a strange pattern: take a mouse, a dog, and an elephant, and their metabolic rates do not scale in proportion to mass but more slowly, as mass to the power of three quarters. An elephant is a million times heavier than a mouse, yet it burns energy not a million times faster but only thirty thousand times faster. Why this is so remained a mystery for nearly a century. This work offers an answer: it all comes down to how oxygen delivery is organized inside the body.
Each holon works like a tiny factory: blood flows through the capillary, oxygen seeps through the wall into the tissue, and cells consume it. The authors set out to optimize this factory: to make the vessels occupy as little material as possible, friction of blood against the walls minimal, and oxygen extracted completely. From these conditions follows a simple rule: blood flow must be proportional to the cube of the vessel diameter. This is Murray's law, known since 1926. The second condition, full oxygen utilization, fixes the capillary length. The result is a perfect building block.
The organism is then assembled from such building blocks. The number of holons in warm-blooded animals is roughly the same, about five hundred million, whether it is a mouse or a whale. The difference in body size is achieved not by adding new building blocks but by enlarging each of them. This is the key idea: an organism's growth is an enlargement of holons, not an increase in their number. In cold-blooded animals, there are ten thousand times fewer holons, which gives them a lower metabolic level.
For small organisms, where oxygen reaches cells mainly by diffusion, the theory predicts a linear dependence of metabolism on mass. For large ones, where convection plays the main role, it predicts a power law with an exponent of 3/4. The transition occurs at a mass where the diffusion time equals the reaction time. This explains why Kleiber's law does not hold for everything: in bacteria and single-celled organisms, metabolism grows in proportion to mass, while in large animals it grows more slowly.
A shrew's heart beats at about a thousand beats per minute, while a whale's beats only ten to twenty times. The theory explains this difference through the number of holons and the volume of blood the heart must pump per beat. The larger the holon, the less often blood needs to be pumped. Thus the same building block, repeated the right number of times, explains metabolic rate, heart rhythm, and lifespan, from mouse to whale.
A shrew's heart beats at about 1000 beats per minute, while a whale's beats only 10-20 times. The theory explains this difference through the number of holons and the volume of blood the heart must pump per beat.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.