(For me: the most.)
Arguments in favor of this proposition include:
In animals, 3/4 scaling applies over many orders of magnitude.
Historically, the applicable mathematical approach depends on dimension: Galileo’s 1638 work on weight-bearing animal bones; Sarrus and Rameaux 1838 on the scaled rate of mammalian breathing; Max Rubner’s and Max Kleiber’s measurements, and the geometric approach in 1997 by West Brown and Enquist.
If the underlying physical relationship prevails at all scales (sizes), then it applies to quanta, to metabolism, to cosmology, and to dark energy.
Or not?
Your views?
Metabolic scaling is the relationship between organismal metabolic rate and body mass. Understanding the patterns and causes of metabolic scaling provides a powerful foundation for predicting biological processes at the level of individuals, populations, communities, and ecosystems. Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the animal's mass. Symbolically: if is the animal's metabolic rate, and the animal's mass, then Kleiber's law states that. On the other hand,allometric scaling is one of the tools that drug developers use to predict human PK based upon animal data. Prediction methods, like allometric scaling, provide a “sneak peek” at how a drug might behave in humans before any clinical studies are conducted.
Quote from:
Does new physics lurk inside living matter? By Paul Davies
Physics Today Volume 73, Issue 8 10.1063/PT.3.4546. August 1, 2020 at p. 40
"Biology is shaping up to be the next great frontier of physics."
Preston Guynn.
Thank you for your added reply, and for mentioning Max Kleiber's 1947 article.
I last looked at Max Kleiber's 1947 article in 2015. Your observations make me want to take a fresh look at it.
The equation you mention is at page 528 of the 1947 article. which he describes as a regression equation.
The 3/4 exponent is dimensionless: that is, no kilograms or kilocalories. He says that the 0.756 regression coefficient in the equation you quotee corresponds (approximately) to the 3/4 exponent of Mass.
Korzybski, who wrote about General Semantics, wrote that Mr. Smith 1920 is not the same entity as Mr. Smith 1930. I think that applies to thinking about physics. The researcher reading an article is 2015 is not the same as the one reading the same article in 2022, if in the interim the researcher has learned some more things. Similarly, a modern physicist in 2022 reading over a physics article written 100 or 150 years ago has the advantage of all the mathematics and physics developed in the interim, which surely holds the possibility of seeing something new in what was written long ago.
I don't recall seeing a similar regression equation elsewhere, I have mainly focused on the exponent of M, which Max Kleiber empirically concluded was 3/4. You pose a good question.
Thank you again for your insights and observations.
Best.
Bob Shour
Preston Guynn
Twenty orders of magnitude seems a significant observation (mentioned by the way at the outset of West Brown and Enquist 1997).
The inverse 4/3 appears in connection with black body radiation. For example, in the derivation of Stefan's Law in Allen and Maxwell at page 743. Energy capacity of radiation (entropy) is 4/3 of that of the container. In metabolic scaling the 4/3 entropy of energy distribution via the circulatory system is balanced by a larger animal's 3/4 scaled slow metabolism.
If the same law that applies to metabolic scaling applies to black body radiation, then the same law may apply to small (atomic) scales and large (cosmological), the possibility raised in your preceding reply.
If that were so, figuring out allometry holds out the promise of figuring lots of other physics.
And, as well, explains why the twenty orders of magnitude you mention appears to be significant.
Best
Bob Shour
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