The Wait But Why blog has an amusing post on why Generation Y yuppies (GYPSYS) are unhappy, which I found through the blog of Michigan economist Miles Kimball. In short, it is because their expectations exceed reality and they are entitled. What caught my eye was that they defined happiness as “Reality-Expectations”. The key point being that this is a subtractive expression. My college friend Peter Lee, now Professor and Director of the University Manchester X-Ray imaging facility, used to define happiness as “desires fulfilled beyond expectations”. I always interpreted this as a divisive quantity, meaning “Reality/Expectations”.
Now, the definition does have implications if we actually try to use it as a model for how happiness would change with some quantity like money. For example, consider the model where reality and expectations are both proportional to money. Then happiness = a*money – b*money. As long as b is less than a, then money always buys happiness, but if a is less than b then more money brings more unhappiness. However, if we consider the divisive model of happiness then happiness = a*money/ b*money = a/b and happiness doesn’t depend on money at all.
However, the main reason I bring this up is because it is analogous to the two possible ways to model inhibition (or adaptation) in neuroscience. The neurons in the brain generally interact with each other through two types of synapses – excitatory and inhibitory. Excitatory synapses generally depolarize a neuron and make its potential get closer to threshold whereas inhibitory neurons hyperpolarize the neuron and make it farther from threshold (although there are ways this can be violated). For neurons receiving stationary asynchronous inputs, we can consider the firing rate to be some function of the excitatory E and inhibitory I inputs. In subtractive inhibition, the firing rate would have the abstract form f(E-I) whereas for divisive inhibition it would have the form f(E)/(I+C), where f is some thresholded gain function (i.e. zero below threshold, positive above threshold) and C is a constant to prevent the firing rate from reaching infinity. There are some critical differences between subtractive and divisive inhibition. Divisive inhibition works by reducing the gain of the neuron, i.e. it makes the slope of the gain function shallower while subtractive inhibition makes the threshold effectively higher. These properties have great computational significance, which I will get into in a future post.