For me, the most beautiful of all mathematical curves is the normal curve. As you may know, it represents a probability density function and hence the total area under that curve is equal to one.
The standard normal curve has a mean (μ) equal to zero and a standard deviation (σ) equal to one.
All of us know that, if we plot the frequency of heights of individuals in a population (from a geographical region) or blood pressure or any other similar quantitative trait, we are most likely to get a normally distributed curve (at least tending towards normal).
Although this is absurd and mathematically incorrect, let us try to equate a human society to the standard normal curve. Let mean be equal to neutral (0) and whatever that tends to +∞ be increasing optimism, and -∞ be increasing pessimism.
Since this is a standard normal curve (mean=median=mode), the number of people who are exactly neutral is the highest. In fact, the probability of finding people close to neutrality (μ±1σ) is 0.68. In other words, nearly 68% of the total population is almost neutral. A small number is either extremely optimistic (in all aspects) or pessimistic.
Similarly, one can define the two extremes as “right wing” and “left wing” (sign is subjective). The scope for new parameters is infinite!
I wish we were in a standard normal society. Nevertheless, some may argue that the society needs to be either skewed or multimodal for it to remain interesting to us. Perhaps, we are in a society whose mean and standard deviation is unkown. As long as the area under the curve is close to one (that is we remain united) I shall be satisfied.
It goes without saying that we do not want to see a negatively skewed society (higher the better) when we plot “tendency towards crime (terror)” or for that matter corruption.
I wish for a day when we plot corruption index of India on a graph sheet, it forms a straight-line curve with a function y=zero.