fuchsbau

Scale, Geoffrey West

(back to books)

---

• Substrat: only few complex systems scale superlinearly (e.g. cities)
  • complex behavior = integration of various simple, repetitive, self-similar behaviours
  • growth = available metabolic energy - maintenance cost
  • ideas and energy cannot flourish without each other
  • greed helps maximise metabolic power relative to size
• organisms scale sublinearly with exponent of 4 (network constraint): aorta lengths 1/4, tree height 1/4, mitochondrial density -1/4, life span 1/4, ...
  • a shrew (4 cms long), a human, a blue whale have same blood pressure/speed (therefore: smaller animals have faster heart beats)
• cities scale superlinearly (open-ended growth because energy increases faster than maintenance costs)
  • gas stations, lengths of pipes/roads/electrical wires scale with 0.85 exponent; wages/patents/GDP/crime/restaurants with 1.15
  • 80-90% of city kpis are due to size
  • relationship scaling factor of ~3 (bond with ~5 people, inner circle ~15, extended circle ~50, casual friends ~150; scales with neocortex volume)
  • cities aren’t driven by profit motive, have distributed power and can balance expenses by raising taxes
• companies scale sublinearly (like organisms)
  • sales (or revenue) of a company is its metabolism, expenses are maintenance costs
  • sales grow linearly with number of employees; expenses scale sublinearly and transition to linearly
  • factoring out overall market growth, large mature companies have stopped growing
  • 23 k of the 29 k (80%) public companies since 1950 died (= no more reporting of sales), roughly 50% of those through M&A
  • after 30 years <5% of a company cohort is still alive (almost 50% die within 10 years); constant mortality rate
  • risk of dying does not depend on age or size (constant mortality rate for company in cohort across years)
  • relative R&D decreases as size increases (administrative expense outpaces innovation support)
• 3 scaling laws: 1) space filling hierarchical networks (e.g. every cell of an organism must be serviced by the network), 2) invariant terminal units as basic building blocks (e.g. capillaries, mitochondria, cells), 3) approximately optimal minimisation of energy needs for energy transmission
• finite time singularity: unbounded, exponential growth requires a) infinite resources or b) (continuously more frequent) paradigm shifts that "reset" the clock before collapse
• Zipf's law: rank order of object is inversely proportional to frequency (e.g. largest city has about twice the population of 2nd largest or largest tree is twice as large as 2nd largest or most common word is twice as common as 2nd most common)
• human subsistence: 90 watts (= 2 k food calories) per day; modern day US-based humans add 11 k watts (from homes, automobiles, roads, computers, ...; >3 k global average), roughly metabolic rate of 12 elephants
• Goethe on the speed of life in 1825: "Everything nowadays is ultra, everything is being transcended continually in thought as well as in action. No one knows himself any longer; no one can grasp the element in which he lives and works or the materials that he handles. Pure simplicity is out of the question; of simplifiers we have enough. Young people are stirred up much too early in life and then carried away in the whirl of the times. Wealth and rapidity are what the world admires. . . . Railways, quick mails, steamships, and every possible kind of rapid communication are what the educated world seeks but it only over-educates itself and thereby persists in its mediocrity. It is, moreover, the result of universalization that a mediocre culture [then] becomes [the] common [culture]. . ."