Assumptions — Bad Assumptions
The Gaussian distribution is based upon a distinct set of assumptions. The first is that ascribed labels matter. If a label is assigned to something, the assignment will be accurate within two or three standard deviations, and that’s good enough. The second assumption is that whatever we’re encountering in the world obeys the law of large numbers. This states that large numbers drift toward obeying the Gaussian distribution. But, it is the third assumption that is the most critical. The real underlying assumption of a Gaussian distribution is that events are independent and truly random (in a mathematical sense). We don’t live in that kind of world. Rather, events are at least partially correlated, and usually not fully independent. What we believe to be random is some illusion of randomness — the patterns do not match the mathematical definitions of true randomness. As a result, random as the layman sees it is not really the random of mathematics on which the distribution depends, instead there are elements of connectedness and mathematical deviations from the true random. We misunderstand the law of large numbers to suggest that when we see noise, it’s noise. Complexity theory suggests that “noise” might be a weak signal of something else. The law of large numbers makes no room for weak signals. The problem with ascribing a label, and using it as your method of explanation, is that once one has ascribed it, once one has said this belongs to Label X, then the explanation is done. There’s no room in that ascription for emergence. Yet, emergence happens. If you shift your scale, if you shift your context, if you encounter something new, one might spend a lot of time trying to make the old ascribed label fit. If you are the “explanation is the assignment of a label” kind of person, you don’t spend time trying to understand the emergence that has just occurred.
