I was playing with a spreadsheet on google docs and eventually started to think about my old high-school math classes and varying kinds of equations and I got to thinking about the old "Beginners talk tactics, Experts talk logistics" addage from the Napoleonic wars.



I ended up creating this equation that describes the logic of a managed society that aims to create a surplus of food rather than to meet the immediate needs of the current residents. I'm very sorry if i make this seem unapproachable, with a little self confidence and some persistence you might get to the point, otherwise it's really only a sort of whimsy and a good example of how much thinking is too much!



(a + a2) = b (ca) = c



where a = food, b = time and c = people.



basically what it means is that if you don't factor for the passage of time, by the time you've grown enough food for your people a lot of them have starved!



anyone care to discuss this idea?

Its not an equation if it has 2 equals signs, to my knowledge anyway.

it's what they call a logical equation, they're usually much simpler (ie. eat + sleep + walk = healthy).

Well, rather it's several equations. Namely:



[LIST=1]

(a + a2) = c

(a + a2) = b (ca)

b (ca) = c

[/LIST]





Secondly, I'd rename b as t, since it's normal nomenclature.

Thirdly a2 is food overproduction, so a is the basic need?



Let me reformulate this so it is a lot more accessible. Basically you say:

[LIST=1]

food + overproduction is population

food + overproduction is the populace' need for food over time

the populace' need for food over time is equal to population

[/LIST]



That's how I interpret it, though I tend to disagree to start with logical formulations when we can paraphrase it exactly. Rather I'd formulate your problem this way:



The need of food depending on the population shall be f(pop), the food production per population f[SUP]+[/SUP](pop) and time t. Everything per turn or arbitrary time interval.

If you want to paraphrase the food production surplus S, you have in a turn the equation:

f[SUP]+[/SUP](pop) - f(pop)=S

This equation is in turn dependent on the population, so let's call it S(pop). If we now say that the requirement for a new population unit to be generated is a fixed amount of food (like in the game) pop[SUP]+[/SUP], you could formulate this logically like:

if( S(pop) dt >= pop[SUP]+[/SUP] ){

pop -> pop+1

t' = t - present turn

S(pop) dt -> |S(pop) dt - pop[SUP]+[/SUP]|+S(pop+1) dt'}

In words: If over time (dt) more overproduction is accumulated than needed for the new population unit to be generated, you gain 1 population unit and lose the necessary amount of food from the overproduction. Then you get new values for S(pop+1) and the rest of food from the previous round.

Now if you want to make this more complicated, you could think of rotting food, nonlinear functions in any of the basic functions, make pop[SUP]+[/SUP] dependent on the population and so on.



At least that's the simplest mathematical way to paraphrase a function for population growth by food I come up with at 23 o' clock.



If you want to keep the population growing, you just have one requirement to add in, the inequation:

f[SUP]+[/SUP](pop) > f(pop)