I would like to define a scale, ranging from -10 to +10, which spans the worst possible situation to the best. I choose 10 because it is commonly used as the arbitrary maximum for scales in our base ten centric society, but 100 or 1 would be work as well. So how good can it get? The ultimate measure for a Utilitarian like myself is "happiness of all beings over all time". So +10 would entail an optimum universe, where the integral of the happiness over all beings for the rest of time was maximal; increasing the number of beings beyond the optimum for a given point in time from would lead to some overcrowding and less happiness. Likewise decreasing the population relative to the optimum at a given time would lead to less happiness. It is difficult to imagine what such a universe would be like; perhaps in order to best utilize the available energy, advanced computers may need to simulate the minds of vast numbers of beings. I will deliberately ignore the issue of precisely quantifying happiness for a single being for now.
Moving down the scale, what is the significance of 0? It would be the equivalent of the ultimate emptiness — a universe devoid of life, pleasure, and pain forever. There are other ways to reach 0; for example, there could be a year of happiness followed by a year of equal pain, alternating through eternity to give a net 0 sum.
Furtherest down the scale is -10, the absolute worst. Here there is as much pain from as many beings as possible, throughout time. Visions of a torturous hell come to mind, with machines forcing organisms to remain alive for reproduction and pain.
Now that I have defined the endpoints and the middle of the scale, the next matter is the points between. The simplest idea is to have a linear mapping, so +5 would involve half as much happiness as +10, yet this does not seem very useful. Compared to our everyday reality, +10 seems perhaps unobtainably high, and even half of perfection is too much to expect in the foreseeable future. Suppose we use a logarithmic scale, so +2 is ten times the happiness of +1. The ability of mankind to affect other planets in our own solar system is currently extremely limited, and affecting distant star systems, which number over 70 sextillion (7e22), seems utterly hopeless. Thus, most values of even the logarithmic scale are practically useless, considering that +10 is only ten billion times more happiness than +1. Perhaps a hyper-logarithmic scale, which maps log(log(an absolute happiness)) to a scale value, would work? There, +10 would be a googol (1e100) times the happiness of +1. At least intuitively, that seems like it would provide ample range for all the degrees of happiness of all the possible beings on all the worlds of all the stars for all time, and yet still provide numbers that can be used for our Earthly realm.
Posted by seander at March 27, 2005 12:16 AM