Percolation models - wild fires, pandemics and extinctions
One model helps to explain much of the natural world around us.
The summer of 2020, has been one much of Australia would rather forget, with the east coast experiencing the worst fire season in living memory. And now, that disaster has been thrown from the news as an even bigger crisis sweeps the globe in the form of the Coronavirus pandemic.
A common link between these events are the percolation theory models that are used to understand them.
Air finding a channel through pores in a mask or fire finding a path through trees in a forest reminded Hammersley of water percolating through coffee grounds . If the grounds are packed too tightly , water may not find a path through . When they are loose enough : drip , drip . So Hammersley called his techniques and ideas “ percolation theory . ” Like symmetry — breaking , percolation theory turns out to connect a staggering range of seemingly unrelated systems . (Bahcall, p170)
Safi Bahcall in his book “Loonshots”, writes:
When will a small disease outbreak grow into an epidemic ? Go back to the model of fire spreading from tree to tree . A high wind speed in the forest , blowing sparks quickly from tree to tree , is like a virus that is highly contagious . A high density of trees is like people living close together ( in cities , for example ) . When the infectability and density cross a critical threshold , small outbreaks erupt into epidemics . When they fall below that threshold , small outbreaks die out quickly . That’s the epidemic phase transition . (p170)
The Going Critical post on Melting Asphalt blog Kevin Simpler builds a series of interactive models that illustrate how the various parameters of a percolation model can impact the spread of everything from a virus, to a wildfire, to ideas. Relating to ideas he writes
The network is important in at least two ways. First, preexisting ideas have to make their way into the mind of the inventor. These are the citations of a new paper, the bibliography section of a new book — the giants on whose shoulders Newton stood. Second, the network is crucial for getting a new idea back out into the world; an invention that doesn’t spread is hardly worth calling an “invention” at all.
And so, for both of these reasons, it makes sense to model invention — or more broadly, the growth of knowledge — as a diffusion process.
His fascinating post highlights the importance of immunity, and social distancing and network density on the spread.
We tend to think that if something’s a good idea, it will eventually reach everyone, and if something’s a bad idea, it will fizzle out. And while that’s certainly true at the extremes, in between are a bunch of ideas and practices that can only go viral in certain networks.
Nikki Case uses the same sort of modelling in his interactive post “Parable of the Polygons” in which he highlights how important it is to demand and actively create diversity to have any chance of it flourishing. His illustration shows how small individual biases lead to large collective biases and lack of diversity.
He further explores these models on the Covid-19 post “What Happens Next?” which provides a range of simulations to play with.
For additional interest watch these concepts explained in the Youtube video Simulating an epidemic
Understanding if a change will spread into a major issue or sail through unnoticed also applies to the modelling of traffic jams where again Perculation theory can be applied:
This… framework enables us to identify instantaneously those roads bridging different traffic clusters of higher velocity (with respect to the bottleneck). These bottleneck links … can provide opportunities to improve significantly the global network traffic with minor cost (e.g., improving a single road). Understanding the congestion formation and dissipation mechanisms in a network view through our framework can serve to predict and control traffic, in particular in the future realization of the “smart city.”
Back to bush fires, percolation models help explain in why the recent experience was so dramatically out of control and how given many of the underlying conditions, a fire of this magnitude was a case of when not if. Firstly there was a high fuel load, which you could think of analogously to an unvaccinated population, just waiting for a trigger to spread.
This high fuel load was a result of conditions in preceding years which made traditional burn off techniques dangerous and limiting the amount of growth that could be safely burnt.
Reports have highlighted how the Aborigines were able to manage the land through a series of slow burns
Aboriginal techniques are based in part on fire prevention: ridding the land of fuel, like debris, scrub, undergrowth and certain grasses. The fuel alights easily, which allows for more intense flames that are harder to fight.
The Aboriginal people would set small-scale fires that weren’t too intense and clear the land of the extra debris. The smaller intensity fires would lessen the impact on the insects and animals occupying the land, too, as well as protect the trees and the canopy.
In Australia, fires that are too hot actually allows the flammable undergrowth to germinate more. When early Europeans tried to copy Aboriginal techniques by lighting fires, they made the fires too hot, and got even more of the flammable scrub. So, they tried again. And again.
Wildfires, traffic jams, pandemics, animal extinctions and more, Percolation Theory is a model that helps us better understand the world around us.
Let me know what you think? I’d love your feedback. If you haven’t already then sign up for a weekly dose just like this.
More like this from 10x Curiosity
- Systems Archetypes- Places to intervene — An advantage with using systems archetypes as a problem solving methodology is that places to intervene in the system can be thought through and played with.
- The Multi-Armed Bandit — to explore or exploit? — When faced with a decision to go with what you know or strike out in a new direction, which do you choose?
- Normalisation of Deviance — Normalisation of deviance is a trap in human psychology that has led to many disasters over the years
- Antifragile — Becoming stronger with failure — Antifragile. A thought provoking concept developed by Nassim Taleb in a book by the same name.
- Achieving Diversity — why being unbiased is not enough — Diversity is something we aspire to, but are we paying more than lip service to it? Are individual good intentions enough to achieve a diverse group setting, at work, socially or through the community?
