Normal II

We're Not Gonna Take It

Hey hung up old Mr. Normal

Don't try to gain my trust!

'Cause you ain't gonna follow me any of those ways

Although you think you must

Is it Normal to accept no error?

Normal describes a group (a distribution) where the Mean is equal to the Median. If  everyone agrees, then the Mean will equal the Median. But normal is NOT limited to a Variance of  zero. A uniform normal distribution is the most stable distribution, and it has a Variance of one, not zero. (An aside. The big push for resiliency is because the push for just efficiency, making the Variance zero, is not always wise.  I apologize for linking to myself,  but this is what  I mean by efficiency vs. resiliency. https://dbeagan.blogspot.com/2022/01/resiliency.html)

If the Variance is zero, then everyone agrees. If the Variance is 1, then most people are not 100%, the same, but people are allowed to be different than the Mean. In a normal distribution, 68% of the observations are within one Standard Deviation of the mean.

If you want to approach the absolute,  then you want to make the Standard Deviation (the square root of the Variance) as small as possible. That is what science is all about. You make lots of observations with a decreasing  Standard Deviation until you approach the absolute. The gold standard in most science is 3 Sigma, 3 Standard Deviations, 99.7%. In particle physics, e.g. the weight of an electron, it is 5 Sigma, 99.99994%.

But once you have established an absolute, then there is by definition no error, and the Variance is zero. But you DON’T start by assuming that the Variance is zero. Error is the Standard Deviation divided by the square root of sample size. If you wish to reduce error, then you don’t automatically assume that the Variance is 0, instead you increase the sample size ( the size of the group). Once you are absolutely correct, the sample size will be irrelevant, the Variance will be zero, and increasing the size of the group won’t change that result. But if there is the possibility that you are wrong, then the way to reduce error, approach an absolute, is to increase the sample size of the group.

It is abnormal to say that the Variance IS zero. If things are normal, then the Variance might be greater than 0 and you better increase the group size if you want to reduce error.

Once upon a time, there was no separation between natural (science) and spiritual philosophy. The separation appears to have been a mistake.  Science can inform the spiritual and vice versa.