Absolutely Nothing

 

I’ve Got Plenty of Nuttin’

Oh, I got plenty o' nuttin'
An' nuttin's plenty fo' me
I got my gal, I got my song
Got Hebben de whole day long
No use complainin'
Got my gal,
Got my Lawd,
Got my song!

In Other Words, NOT absolutely nuttin’

Porgy in this song from Porgy and Bess, states that he has nothing on the scale of plenty.  But plenty excludes Heaven, his Lord, his gal, his song, and many other things. Plenty thus must be measured on a relative scale, not an absolute scale.  It is like saying that the temperature is below zero outside. On the absolute Kelvin scale it can by definition never be below zero.  Saying that a temperature is below zero on the Centigrade scale only means that zero on that scale has been relatively set as the freezing point of water. 

Saying that there is a temperature of absolute zero must therefore mean that at the opposite end there is an absolute temperature.  The fact that we have never observed an absolute temperature does not mean that there isn’t one.  There are absolutes that we can observe such as light.  Einstein’s Theory of Relativity says that the speed of light is an absolute that can be approached, but not exceeded.  An exponential equation, including radioactive decay, measures the relationship to an absolute that can be approached, but not exceeded.  The question becomes how many absolutes are there?  An answer is that there is only one absolute, which can be perceived differently, but each perception is only one aspect of a single absolute. If there is only one absolute then if x is measured on an absolute scale then the integral of any function of x, f(x), should not be which ∫_-∞^∞ f(x) dx which implies the existent of two absolutes, infinity and its negative, but instead should be ∫₀^∞ f(x)dx, which implies the existence of only one absolute, infinity and its absence, zero.

This has an implication on the computation of the Cumulative Distribution Function, CDF, for all distributions.  The Probability Density Function, PDF, is defined without consideration of positive or negative x, but the CDF, the integral of that PDF, is then also only defined for x>0, i.e. x less than zero is undefined.  If the PDF is a normal random logistic function, its PDF is 1/(4s)*sech²(0/2s), and its CDF is ½* tanh(0/2s)+1/2.  A physicist might say that if s=0 and 0/0 is defined by its limit as 1, then the PDF is 0 but the CDF is ½, but a mathematician might say that if s=0 and 0/0 is undefined, then both the PDF and CDF are undefined.