Were my memory not still faulty, I would swear I wrote maybe in Maximum Irony that the Central Limit Theorem says that all probability distributions become normal as the number of data points increases, in accord with the Law of Large Numbers.
If I wrote that, I need to correct it. I really must get a system, a 6 sigma Lean-type SOP for catching these errors.
What is worse is that the error is a distraction, no more, as it is probably irrelevant to the argument at hand, that all men are more or less equal, when all properly defined desirable characteristics are given the roughly equal weight that they deserve; that is, if the desirable characteristics are properly defined so as to be roughly equal in importance.
Proper definitions of virtues are also empirical, and thus measurable, and together with the large number of people in the population, that is what gives us the normality in the distributions of the virtues and that is what allows us – given certain other assumptions – to analyze the data using the methods of parametric statistics.
Radical elitisms like that in the Jewish bible, in the ancient Greeks, and in Nietzsche are utter nonsense. The American ideal of equality of all people is well grounded in probability and statistics, properly understood and applied.
Of course that claim about the Central Limit Theorem is nonsense. That was how I remembered it long after taking undergraduate statistics. Faulty memory. Poor understanding. A proper understanding helps a rather poor memory remember what is the correct answer.
The role of arrogance is in my believing in my memory and not looking up the damned theorem again! Not trusting my memory after years have passed, and not trusting my defective understanding of undergraduate statistics is not lack of confidence but common sense. So in the end, I lacked understanding, remembered something incorrectly, wrote it wrong, had the colossal gall not to check it, and displayed an utter lack of common sense that so often accompanies the arrogance.
Wow! And I set myself up as some kind of know-it-all when in truth I know nothing at all.
Re: understanding: Consider the rolling of a fair die. This is a discrete uniform distribution with 6 points, each with probability of 1/6. No matter how many times one rolls the die, the distribution will always be uniform. It never becomes normal.
What becomes normal the more times it is done is the sampling distribution of the mean. The mean of the uniform distribution is 3.5. If one rolls a die “n” times, records the average each time, and repeats this over and over again, what one gets is a normal sampling distribution of the mean, with a mean that is the same as the uniform distribution from which it is drawn, that is, 3.5. This is what the Central Limit Theorem says. Not that the uniform distribution ever becomes normal. That is nonsense.
This time I am positive, yet my memory is so faulty, my understanding so poor, my arrogance so unbounded, and my common sense not equal to what god gave a horsefly.
I hope this time I am not embarrassing myself yet again.
I am hopeless! So is man! Flawed to the mentally defective and rotten core of our being!