Discontinuities

 

Go to the Mirror, Boy (See Me, Feel Me, Touch Me, Heal Me)

I often wonder what he is feeling
Has he ever heard a word I’ve said?
Look at him in the mirror dreaming
What is happening in his head?

Maybe our universe IS inside the mirror.

The original Star Trek ( yes, I am that nerdy), had an episode Mirror, Mirror where Captain Kirk entered an evil mirror universe ( the one with Spock with a Goatee!).  Our universe appears to be hyperbolic https://dbeagan.blogspot.com/2022/07/forever.html. It may also be that evil mirror universe.

Random events appear to follow an exponential distribution.  Those random events, and that statistical distribution, are constrained to real positive values.   This may be a limitation of our universe.  If negative numbers are allowed AND the negative distribution is a mirror of the positive distribution instead of being confined to positive numbers, there is a discontinuity at the origin.  In other words, the Probability density function, PDF of the exponential distribution for all values of x, not just x>0, may be

(x≥0)*(λ*e^-λx) + (x<0)*( λ*e^λx)

and the Cumulative Distribution Function, CDF, for all values of x, not just x>0, may be

(x≥0)*(1-e^-λx) + (x<0)*( 1-e^λx )

When the traditional exponential distribution, the portion with non-negative values of x,  is combined with a logistics distribution, as proposed by Jimmy Reyes, it appears to be to be a better fit to a normal distribution, but it has a pseudo peak in the negative domain, which becomes positive when the standard deviation (tolerance) becomes very small.  Is it possible that negative and positive are just our perceptual biases and that we are really living in a universe where entropy increases (and remember one of the names for Satan is the Lord of Entropy) and that the fate of energy is that it will all be exhausted and transferred to Entropy.  On the other side of the discontinuity, in a mirror universe to ours, is it possible that Entropy (evil) is decreasing?