Stories

 

Camelot (reprise)

Ask every person if he's heard the story,
And tell it strong and clear if he has not,
That once there was a fleeting wisp of glory
Called Camelot.
Camelot! Camelot!
Now say it out with pride and joy!

What is important is the story!

My heroes are Shakespeare, Shaw, Bob Dylan, Cole Porter, Joni Micthell, Picasso, Frank Capra, among many, many others. I wish that I could tell stories like they do with words, songs, or pictures. But that is not how I roll. My stories use numbers and variables, mathematics, but they are stories nonetheless. And I would like to believe that those stories are important and add to the glory too!

Stories are important because they require imagination. And while we live in a real world where the coefficient of imagination is zero, that does NOT mean that imagination does not exist. If it does exist and has to be considered, then the implications are tremendous.

Imagination might be why randomness, entropy, gravity, etc. exist in the first place. We ignore imagination at our peril. It is convenient to pretend that the square of any number, x², should be solved by simply taking its square root, but the square root is only real if imagination is NOT considered. Take the variance, σ², for example. It is often assumed that the Standard Deviation, SD, is the square root of the variance. But this is strictly only true for flat, Euclidean, surfaces. In the surface is flat, then the variance is σ²= (SD)² +0²*i does indeed have the solution, SD=√σ², but is only because on a flat surface cos(σ)=cos(SD)*cos(0). On a hyperbolic surface it should be cosh(σ)=cosh(SD)*cosh(0). This does NOT become a single value but two values, σ=ln(cosh(SD)±sinh(SD)). When sinh(SD) is very small, that term  can be ignored and then the mid point of this range approximates SD = √σ². It is appropriate to think of the term cosh(SD) as the location, µ, parameter in a random equation where the range parameter, the standard devation , σ, sinh(SD) is the other parameter.

The problem is that no number is exact. There is always a Standard Error term, SE. The definition of SE is SD/√n, where n is the size of the sample population. If there is growth, a value that is outside those values range, then a Growth Factor, GF, has to be applied to the values to include that growth, GF*(x-SE)<y<GF*(x+SE). X is the average, mean, value of a series of numbers, corresponding to the sample population, (∑x_i)/n. If n, the sample size of the population has not changed, then the Growth Factor should only be applied to every value of x_i.  If the Growth Factor is also applied to SE, and if the sample population has not changed, then it has to be applied  to the SD. This new SD may now have become so large that the uncertainty of the range can no longer be ignored. Otherwise, to keep the Standard Error the same, the size of the population has to be decreased.

Sounds like the “rINO, republicans IN Name Only” response to growth, decreasing the size of the population? The problem is that if the size of the population is decreased, then the location term, µ, has to decreased by even more because it is divided by n not √n. So you get into a mathematical death spiral. In order to accommodate growth, without increasing error, you have to constantly decrease the size of the population.

Mathematics is a harsh mistress, and imagination is ignored at all of our peril. That is my story, and I am sticking to it!