From Cells to Cities Part 1 – Biological Scaling (Geoffrey West)

Cells to Cities

Waking Up with Sam Harris #86 – From Cells to Cities (with Geoffrey West)

In this episode of the Waking Up podcast, Sam Harris speaks with Geoffrey West about how biological and social systems scale, the significance of fractals, the prospects of radically extending human life, the concept of “emergence” in complex systems, the importance of cities, the necessity for continuous innovation, and other topics.

This post is part one of three of this illuminating ‘Waking Up’ podcast. ‘From Cells to Cities’ deals with aspects of life that we rarely consider yet are intrinsically part of who we are and the environment in which we live. It is so overwhelmingly relevant and cutting edge, I felt compelled to write excerpts as a personal development exercise so I could internalize it.  This is my attempt to do that. Such is the plethora of vital information therein, I had to split this exercise into 3 parts.

Some of what is written below is verbatim and some of it is redacted slightly to be more reader-friendly:

Part 1 – Biological Scaling

If you are starting to think about aging and mortality, you have to start thinking about what is going wrong in terms of keeping you alive. What wears out and starts to become dysfunctional?
What is really keeping you alive is metabolism. You eat and metabolise food for energy. But before we get into that, lets look at scaling laws.

MycoplasmaOrganisms: Smallest organism: Mycoplasma is a tiny sub bacteria organism. A parasitic bacterium which lives in the primate bladder, waste disposal organs, genital, and respiratory tracts.
Largest: Blue Whale
The order of magnitude between the smallest and largest is 20 order of magnitude or 20 powers of ten. This is even a much greater scale than say the relationship of us to the entire Milky Way. Or an electron to a cat. So the order of magnitude as part of this life span is far greater than one might presume.

Scaling laws (The phenomenon of scaling)
How does a mammal’s characteristics scale as you change the size of the mammal? The smallest mammal is the shrew and the largest the blue whale. That covers 8 orders of mass. Now if we look at the metabolic rate… That is the amount of energy any organism needs per second, per hour to stay alive. So then how does that metabolic rate scale with respect to the size of the mammal?

Lets look at characteristics of these mammals such as the metabolic rate, length of aortas (the main artery that comes out of the heart), the size of hearts, or the length of limbs. Also how long do they live and how many offspring do they have? One could list 50 or 75 of such characteristics. But how do they change with the size of the animal?
The remarkable thing when you look at any of these quantities is they all scale in a regular fashion; in a similar way mathematically. You might have thought due to evolutionary reasons such as natural selection that if you plotted these characteristics such as metabolic rate versus size of mammal you would get points scattered all over the graph. On the contrary, there is tremendous regularity underlying this extraordinary complexity such as that of metabolism. So if you ask how it scales across this huge range of organisms – it can be expressed mathematically and conceptually in simple terms.

The Nature of Biological Scaling
If you look at an organism that is twice the size of another one, such as a mammal then it contains roughly twice as many cells. That is linear scaling and it is roughly correct. However, the scaling of all other characteristics of mammals are non linear. For example, regarding metabolic rate, if you double the size of an organism; instead of getting twice as much energy, requiring twice as much food to stay alive what you in fact need is 75% as much although there contains twice as many cells. This happens systematically, so if you double the size from 4 grams to 8 grams you only need 3/4 the amount of energy. There is a 25% saving, every time you double the size. That is called a classic economy of scale. It means the individual cells which is linear to scale require 25% less energy. So as a human your cells work less hard than your dog or cats, but your elephant or horse are working even less harder than you.

This is a pervasive phenomena in biology and biological scaling laws.  This economy of scale has far reaching consequences. That similar kind of scaling gets repeated across any measurable quantity whether its physiological, like the length of an aorta, or something sophisticated like the rates at which oxygen diffuses along membranes or how long an organism lives and so on. These are governed by this 25% rule. Time scales increase also, so the bigger you are the more the pace of life slows down. So looking at an elephant and following these scaling laws; if you ended up scaling down you would end up with a mouse. With respect to the nature of this scaling, a mouse is a tiny elephant. However these laws are not like the laws of physics. They are not as precise like Newtons Laws where we can calculate and predict things in a highly precise fashion. That is not true of the kind of scaling laws discussed here in biology. These scaling laws are course- grained in their modeling in that they are only true with 80 – 90% accuracy.

If you give me the size of the mammal I can tell you just about anything about it. Its metabolic rate, the complete structure of its circulatory system or respiratory system, how long it will live and how many offspring it will have, but only with 80 -90% of accuracy. So generally speaking it’s relevant for the average animal of that size.  That’s still extremely powerful because it connects these organisms which live in different environments by providing a baseline using the scaling laws.

Interestingly, the same scaling laws apply to trees and plants. The way the trunk of a tree scales is identical to our aorta. The analogue to the tree inside us is our circulatory system. The analogue to our aorta is the trunk of the tree. What is the origin of these scaling laws? What is it that’s common amongst plants, trees, birds and mammals etc. They all seem to obey the same scaling laws although the engineering and design is different. What’s common amongst all of them is they have hierarchical branching network systems that deliver oxygen and nutrients from a central reservoir all the way down to the cellular level.

These networks also have universal properties one which is called space-filling. Whatever the structure of the network, for example our circulatory system, its terminal units are capillaries which feeds the cells. These capillaries have to go everywhere because every cell has to be fed by oxygen diffusing blood from capillaries to cells. The end points of the network have to be close by the cells.  So the network in that sense has to be space filling not unlike how road networks function within a city. The road networks have to service all buildings and ultimately all people. The street system doesn’t leave vast array of houses without any access to them. So it is with the circulatory system within our bodies. Fundamentally, our circulatory systems minimise the amount of work our hearts have to do to pump blood and feed cells. So this allows us to maximise the amount of energy we can devote to whats called Darwinian Fitness; having sex and rearing children. Such is the complexity and efficiency of the structure of the network is that if we changed it in any significant way such as doubling the third branch of your arterial system that would increase the amount of energy your heart would have to do.

This continuous feedback process inherit in natural selection signify that mammals which have survived tend towards this optimisation and minimisation of the energy and thereby maximising the amount put into their genes going forward ie Darwinian fitness. This optimal system is fractal like – self similar. The fractality of a tree for instance; if you cut some branch and remove looks like a little tree. Then you can cut a branch of that and it looks like an even smaller tree. That’s the idea that you have with this repetitive self-similarity. All of these systems have this fractal regularity which permeates nature, that something is being optimised.

Fractal BiologyNot only are fractals in the world all around us – they are even inside us! In fact, many of our internal organs and structures display fractal properties.

So each of our lungs are the size of a football, but the surface area of the respiratory membranes is the size of a tennis court because of how endlessly branching it is. If you laid out all the vessels in your circulatory system end to end you would go round the earth more than once.

Related Articles:
1. From Cells to Cities Part 2 – Life Span (Geoffrey West)
2. From Cells to Cities Part 3 – Cities and Growth (Geoffrey West)

“The more I live, the more I learn. The more I learn, the more I realize, the less I know.”- Michel Legrand

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