When I was researching whether there was a common law for all living things on Earth, I came across the number 3/4. So there is such a thing as a natural law of body size. There is a correlation between an animal’s weight and the weight of its brain, and this applies to a 2,700 kg elephant and a 19 g mouse. The weight of the brain seems to be proportional to the 3/4th power of the body weight, which is called the 3/4 power law. It seems that humans have larger brains, but even so, this law still applies broadly. I wonder why it is 3/4. It’s strange.
https://www.toho-u.ac.jp/sci/bio/column/0827.html
There is also Kleiber’s law, which states that an animal’s metabolic rate is proportional to the 3/4 power of its body weight, or that an animal’s respiration rate is proportional to the 3/4 power of its body weight. This also applies to large plants. The 3/4 power calculation is a rough idea, but it seems that the larger the size (heavy the body weight), the slower the respiration, and the smaller the size (lighter the body weight), the faster the respiration.
https://www.gizmodo.jp/2013/02/post_11560.html
Such a correlation between two elements, regardless of the size of an organism’s body, and when both are expressed in logarithms, is called allometry. The formula that was successfully extracted seems to be highly versatile. Also, although it is not a 3/4 power, there seems to be something called Richardson’s 4/3 power law. This is a theory that turbulence in the ocean and atmosphere increases the speed of diffusion over time, and the diffusion coefficient increases as the 4/3 power of time.
https://www.ms.u-tokyo.ac.jp/sgw/2018feb.html
I’m curious as to why those numbers were chosen, but there are also other numbers related to 3/4 and 4/3.
Radio waves seem to bend toward the ground due to the curvature of the Earth, but if we were to hypothetically increase the radius of the Earth, radio waves would travel in a straight line, which would simplify various calculations. This hypothetical Earth is 4/3 times the size of the real Earth, and is called the equivalent Earth radius coefficient.
https://www.ieice.org/cs/ap/misc/denpan-db/prop_model_db/model_list/spherical_earth_diffraction
These are the refractions of radio waves, but the refraction of water also has a ratio of 3:4. Objects in water appear 4/3 times larger than their actual size and 3/4 closer to them than their actual distance.
http://www.sugipro.co.jp/kouza/contents/hikarinokussetutohansya.html
The volume of a sphere = 4/3 x radius ³ x π may have something to do with it, but when a simple number appears in the midst of such a complex natural process, it feels interesting, as if there is some universal principle. The law of 3/4 is amazing. The Earth, which has universal principles, is amazing.
