Error

 

Oops I Did It Again.

Oops, I did it again to your heart
Got lost in this game, oh baby
Oops, you think that I'm sent from above
I'm not that innocent

Being human is not being innocent.

To err is human, To forgive is divine. Being divine is being innocent. Since I am human, as are you, I expect there that will be errors. The Standard Error is expressed mathematically as Standard Error= σ /√n, where σ is a statistical measure of the distribution called the variance, and √n is the square root of the number of observations, n. In the real-world n has to be less than infinity so √n also has to be less than infinity. If the variance is real and not zero, then the standard error can NOT be zero. So when we say there is an error, we are saying that the variance has to be greater than 0.

Absolute truth means that there is NO error. If there is no error then the variance must be zero. If there is error then the variance has to be greater than zero. For a given variance, one way to reduce the error is to increase the number of observations. That is why when pollsters want to decrease their error, they increase the number of observations.

One would think that if there is an absolute there can be no error. Albert Einstein’s Theory of General Relativity answered this apparent contradiction. (Actually Jesus addressed the same thing in that whole “Render unto Caesar” gig.). There can be an absolute truth, e.g. the speed of light, and yet depending on your frame of reference, things like length, weight, time, all depend on your relationship to that absolute. The variance is greater than zero. No matter how many observations you make, if there is an absolute truth, only one observation should be enough and  the variance is zero. In a group, if there is no variance, then the mean of the group is equal to the median. However the mean can be equal to the median any time the variance is greater than than zero if the skew is also zero. In fact a normal distribution is any distribution in which the mean and the median are equal. A uniform normal distribution is one in which the variance is 1. If the variance is 1, then the Standard Error has to be greater than zero, even if there is only one observation:  Standard Error = 1/ √1. You can make the error smaller if you increase the sample size, increase n, but mathematics says that you can never can  eliminate the error. You’re not that innocent.