CONCEPT
Quarter-Power Scaling
The family of scaling laws — exponents that are all multiples of one-quarter — that governs biological variables across twenty-seven orders of magnitude, from heart rate to lifespan to DNA repair rate.
Quarter-power scaling is the broader family of laws of which Kleiber's law is the most famous member. Metabolic rate scales as mass to the positive 0.75 power. Heart rate scales as mass to the negative 0.25 power. Lifespan scales as mass to the positive 0.25 power. Aorta diameter, rate of DNA repair, density of mitochondria, reproductive rate — dozens of biological variables, measured across species spanning ten orders of magnitude from shrews to whales, fall on straight lines when plotted on logarithmic axes, and the slopes of those lines are always multiples of one-quarter. The universality of quarter-power exponents across such diverse biological quantities was the pattern that convinced West an underlying principle must be at work. The fractal branching network derivation explains why: any system optimizing resource delivery under space-filling, terminal-invariance, and energy-minimization constraints must produce exponents in multiples of one-quarter.
In The You On AI Field Guide
The pattern is remarkable in its breadth and its precision. Consider the coupling between