Almost anything can be governed by a linear systems of equations. One example could be monitoring the population of a city/state/country, like how much people come to visit or how much are being born. It would be difficult to put a conservation law on the general population but if we can try to use a conservation law on a smaller portion such as the amount of people that travel then we could simplify our calculations. This can be similar to another system in the way that we have to start with a conservation law, and design or model the system to fit what we need. After defining our system we can use a conservation law that applies and try to get a differential equation or a linear equation to obtain our solutions. Systems have the same ideal process in obtaining information but the equations could be different. Such as a volumetric problem may differ from our population problem. The volumetric problem could deal with air, or water being inserted or distributed which would create a mass flow rate equation. Although the mathematics behind it might be the same, where we could eliminate the differential part if there is no change. Either way we start by playing physicists, then mathematician, and then engineer to figure out the solution(s). The steps are similar but the details of the solution may differ.
I agree that approaching population through conservation laws would be a difficult challenge, but it would probably be something tangential to conservation of food or other resources. It would definitely be interesting to try to work a model of that out, although probability would play a larger roll than the normal rigidity of physics we're used to.
ReplyDeleteI agree entirely, I believe probability would play a huge roll as well. There is always the probability of a natural disaster hitting, but that is also including in picking the model (Philadelphia). Another possibility could be a change in jobs, they might hate having to commute far distances. I agree the amount of possibilities are endless but that might be a cool idea to test. What if the possibilities cancel themselves out. There was an even amount of possibilities.
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