Ordinary Differential Equations and bitcoin mining
Calculus is the language in which God wrote the universe. Differential equations exist everywhere in nature. An example is the predator prey model (Lotka–Volterra equation). The population of rabbits grow; as there an increased supply of prey for the foxes to eat so the population of the predator (foxes) also grow. This of course creates a problem. The foxes grow up and require more food thus reducing the population. As the supply of food decrease the fox population will also decrease due to starvation.
We also notice there is a lag. We also observe this in nature in incubation periods or breeding seasons.
In bitcoin world, we see this relationship with miners and difficulty. Difficulty is the product of how much hashing the miners are doing. Conversely, if the difficulty drops creating bitcoins becomes easier; so more miners come on board.
There is however another system we should investigate. As the price of bitcoin increases so too is the attractiveness of mining, so more miners come on board. The lag we see in nature also occurs here too, as hardware suppliers struggle to fill the demand.
So far mining hashing has been growing exponentially. Prices on average have been growing too until recent times. Prices are now 1/3 of their $1,200 high. Difficulty has risen 4 times too. This is not a good position for the large mining companies that have sprung up recently. Their costs are growing and returns are shrinking. This isn’t sustainable.
Will we see large miners go bust and suddenly switch of large amounts of hashing? Only time will tell.