๐ฆ๐ฐ๐ฎ๐น๐ฒ: ๐ง๐ต๐ฒ ๐จ๐ป๐ถ๐๐ฒ๐ฟ๐๐ฎ๐น ๐๐ฎ๐๐ ๐ผ๐ณ ๐๐ถ๐ณ๐ฒ, ๐๐ฟ๐ผ๐๐๐ต, ๐ฎ๐ป๐ฑ ๐๐ฒ๐ฎ๐๐ต ๐ถ๐ป ๐ข๐ฟ๐ด๐ฎ๐ป๐ถ๐๐บ๐, ๐๐ถ๐๐ถ๐ฒ๐, ๐ฎ๐ป๐ฑ ๐๐ผ๐บ๐ฝ๐ฎ๐ป๐ถ๐ฒ๐ ๐ฏ๐ ๐๐ฒ๐ผ๐ณ๐ณ๐ฟ๐ฒ๐ ๐ช๐ฒ๐๐
This book is a wonderfully cross-disciplinary exercise in fractal discovery and insight onto our world - initially the result of the author's pondering mortality which led to a study of longevity across organisms, and then expanded to social structures like cities and companies.
In the book, โscale" itself, conceptually, is defined as "How systems respond to changes in size." Does doubling an animal's dimensions increase its relative strength? Does doubling a city's size double it's relative rate of crime?These 2 questions introduce the key distinctions of ๐จ๐ช๐๐ก๐๐ฃ๐๐๐ง scaling (the larger the thing, the relatively less of some characteristic it has) and ๐จ๐ช๐ฅ๐๐ง๐ก๐๐ฃ๐๐๐ง scaling (the larger the thing, the relatively more of some characteristic it has), respectively.
Organisms, we discover, scale sublinearally - larger animals are more efficient requiring less energy per unit of weight, but similarly they become, relatively, structurally weaker as size increases - this is why Godzilla cannot exist, he would collapse under his own weight! Further, biological metabolic rate scale sublinearlly to size, so as the organism grows, energy demands of cellular maintenance outstrips supply leading to cessation of growth and eventual death (we also find companies face a similar fate, with "costs" replacing cellular maintenance).
Cities, however, are more interesting. In terms of infrastructure they scale like organisms (sublinearlly), but in terms of emergent human outputs, they scale superlinearlly - the larger the city, the relatively more patents, companies, GDP, crime, and disease it will host. For cities, superlinear scaling of those emergent human properties, or "social metabolism" results in the creation of social capital increasingly outpacing the demands of maintenance (those being largely infrastructural) suggesting accelerating, unbounded, open-ended growth.
With regard to growth, superlinearity results in exponential growth, which the authors approaches as something of a revelation of dark mathematical honor. He illustrates this with what I found to be one the book's most illuminating vignettesโฆ
๐ฆ๐๐๐ก๐๐ฅ๐๐ข: It is 11:00. A petri dish ๐งซ contains a single bacteria๐ฆ cell. This bacteria will double every minute. The petri dish will be completely full in 1 hour. At what time is the petri dish ๐งซ 50% full?
If you said anything other than 11:59, you've missed the key implication of exponential growth. Exponential growth is ๐จ๐ก๐ค๐ฌ๐ก๐ฎ, ๐ฉ๐๐๐ฃ ๐๐ก๐ก ๐๐ฉ ๐ค๐ฃ๐๐. But letโs double down on this to really underscore that point - at what time does the petri dish in the aforementioned scenarios become just 1% full? The answer is somewhere between 11:53 and 11:54. Reflect on that.
What might this kind of acceleration in growth mean for technological advancement, for population, for resource consumption and for how they all relate to each other? Thankfully, the book rejects Malthusianism, while still raising legitimate questions about the math of exponentially expanding earthbound civilization sustainability, and calls to an imperative to harness nuclear and solar energy at-scale as our best hopes.
Finally, the examination of exponentiality brings us to the deepest conundrum identified in the book - the ๐๐๐ฃ๐๐ฉ๐ ๐ฉ๐๐ข๐ ๐จ๐๐ฃ๐๐ช๐ก๐๐ง๐๐ฉ๐ฎ - where unbounded growth cannot sustain without either (1) infinite energy or (2) paradigm shift "reset" staving off collapse. But wait! There's more! The mathematics of superlinearity suggest that, in absence of infinite energy, the absolution of paradigm shift resets are themselves required to happen at faster and faster pace, or shorter and shorter intervals.
So, if we are confined to earth's closed system, the need for continuous, stacked, paradigm shift innovations at ever-shorter intervals eventually manifests a meta-finite time singularity, the ๐๐จ๐จ๐๐ฃ๐ฉ๐๐๐ก ๐จ๐๐ฃ๐๐ช๐ก๐๐ง๐๐ฉ๐ฎ which is perhaps, inescapable. The core insight to be extrapolated here is that if we are to overcome the singularity trap, we must drive real, constant step-function innovation and that this innovation must, almost necessarily, allow us to progressively harness orders of magnitude more energy than today - think Dyson Spheres and interstellar travel.
๐๐ข๐ก๐๐๐จ๐ฆ๐๐ข๐ก: Dense yet whimsical, lengthy yet fun. Questing and questioning cover to cover. Great for anyone interested in inter-disciplinarianism and fractal thinking (the long practice of which I find lends to heightened levels of predictive intuition) (4/5โข๏ธ)
https://www.amazon.com/Scale-Universal-Growth-Organisms-Companies/dp/014311090X
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