This reminds me of a talk by Peter Railton I attended several years ago. He described happiness as a kind of delta function: we are as happy as our difference from our set point, but we drift back to our set point if we don’t keep getting new input. Increasing one’s set point will make one “happier” in the way you seem to be using the word, and it’s probably possible (we already treat depressed people, who have unhealthily low set points and are resistant to more customary forms of experiencing positive change in pleasure).
Making explicit something implicit in steven0461′s comment: the term “delta function” has a technical meaning, and it doesn’t have anything to do with what you’re describing. You might therefore prefer to avoid using that term in this context.
(The “delta function” is a mathematical object that isn’t really even a function; handwavily it has f(x)=0 when x isn’t 0, f(x) is infinite when x is 0, and the total area under the graph of f is 1. This turns out to be a very useful gadget in some areas of mathematics, and one can turn the handwaving into actual mathematics at some cost in complexity. When handwaving rather than mathematics is the point, one sometimes hears “delta function” used informally to denote anything that starts very small, rapidly becomes very large, and then rapidly becomes very small again. Traffic at a web site when it gets a mention in some major media outlet, say. That’s the “Dirac delta” Steven mentioned; the “Kronecker delta” is a function of two variables that’s 1 when they’re equal and 0 when they aren’t, although most of the time when it’s used it’s actually denoting something hairier than that. This isn’t the place for more details.)
We only occupy a level of happiness/contentment above our individual, natural, set points as long as we are regularly satisfying previously unsatisfied preferences. When that stream of satisfactions stops, we gradually revert to that set point.
This reminds me of a talk by Peter Railton I attended several years ago. He described happiness as a kind of delta function: we are as happy as our difference from our set point, but we drift back to our set point if we don’t keep getting new input. Increasing one’s set point will make one “happier” in the way you seem to be using the word, and it’s probably possible (we already treat depressed people, who have unhealthily low set points and are resistant to more customary forms of experiencing positive change in pleasure).
So happiness is the difference between your set point of happiness and your current happiness? Looks circular.
What do you / did he mean by delta function? Dirac delta and Kronecker delta don’t seem to fit.
Delta means, in this case, change. We are only happy if we are constantly getting happier; we don’t get to recycle utilons.
Making explicit something implicit in steven0461′s comment: the term “delta function” has a technical meaning, and it doesn’t have anything to do with what you’re describing. You might therefore prefer to avoid using that term in this context.
(The “delta function” is a mathematical object that isn’t really even a function; handwavily it has f(x)=0 when x isn’t 0, f(x) is infinite when x is 0, and the total area under the graph of f is 1. This turns out to be a very useful gadget in some areas of mathematics, and one can turn the handwaving into actual mathematics at some cost in complexity. When handwaving rather than mathematics is the point, one sometimes hears “delta function” used informally to denote anything that starts very small, rapidly becomes very large, and then rapidly becomes very small again. Traffic at a web site when it gets a mention in some major media outlet, say. That’s the “Dirac delta” Steven mentioned; the “Kronecker delta” is a function of two variables that’s 1 when they’re equal and 0 when they aren’t, although most of the time when it’s used it’s actually denoting something hairier than that. This isn’t the place for more details.)
This doesn’t make logical sense if both these words “happy” mean the same thing, so we should use different words for both.
We only occupy a level of happiness/contentment above our individual, natural, set points as long as we are regularly satisfying previously unsatisfied preferences. When that stream of satisfactions stops, we gradually revert to that set point.
OK, so the point is happiness depends on the time derivative of preference satisfaction rather than on preference satisfaction itself?
If I knew what “time derivative” meant, I might agree with you.
Amount of change per unit of time, basically.
Then yes, that’s exactly it.
You can think of happiness as the derivative of utility. (Caution: That is making more than just a mathematical claim.)