Shit! Life is harder than my miderms!*
*Or, dear god, no wonder people don't behave perfectly rationally all the time. Even though the subconscious is a lot better at doing this than I am.
Given:
~aloneness + raininess = getting up late = eating weird foods at weird times = blood sugar level = -(sadness) = wishing to be alone at t+1. (All positive coeffients have been left out for simplicity) Not all variables are measured on a linear scale and aloneness, raininess, sadness, and (wishing to be alone) can be negative. Notationally, all subscripts on variables denote time with start time = t.
~aloneness is a positively correlated with energy at time t --> aloneness = (energy sub t) + (likable, known people in the immediate vicinity)
~ however, energy sub t = f(aloneness sub t-1) + tiredness
~where tiredness = if (sleep debt over the last week) >= alpha, tiredness = 1 and if not, tiredness = (8 - hours slept the night before/8)
~happiness = -sadness
~Raininess (for simplicity) is distributed N(0,sigma squared)
~utility = happiness at time t + (discount factor)happiness at time t+1 + (discount factor)^2 happiness at t+2... , where happiness is a function of enjoyment and -(energy spent) and a disount factor between 0 and 1.
Find:
~energy (wrt the the least number of other factors) to maximize utility
Given:
~aloneness + raininess = getting up late = eating weird foods at weird times = blood sugar level = -(sadness) = wishing to be alone at t+1. (All positive coeffients have been left out for simplicity) Not all variables are measured on a linear scale and aloneness, raininess, sadness, and (wishing to be alone) can be negative. Notationally, all subscripts on variables denote time with start time = t.
~aloneness is a positively correlated with energy at time t --> aloneness = (energy sub t) + (likable, known people in the immediate vicinity)
~ however, energy sub t = f(aloneness sub t-1) + tiredness
~where tiredness = if (sleep debt over the last week) >= alpha, tiredness = 1 and if not, tiredness = (8 - hours slept the night before/8)
~happiness = -sadness
~Raininess (for simplicity) is distributed N(0,sigma squared)
~utility = happiness at time t + (discount factor)happiness at time t+1 + (discount factor)^2 happiness at t+2... , where happiness is a function of enjoyment and -(energy spent) and a disount factor between 0 and 1.
Find:
~energy (wrt the the least number of other factors) to maximize utility